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What makes a brand a brand, and ? As a marketer, I know that thinking — let alone talking — about aspects of branding and how to manage a brand identity successfully, can get a little muddy, and remain somewhat superficial. In this article we’re going to go beyond logos, color codes and fonts, and talk about the elements at the core of brand identity, brand success and effective brand management. what makes a successful brand In branding, style is frequently confused with substance. — Wally Olins What is a brand? What are the first things that usually come to mind when we think or talk about branding and brands? Well, usually we’ll think about annoying online ads, or we'll jump right into the visual aspects of a brand. We’ll think about examples such as Nikes’ swoosh logo or Apple’s, well, apple — but also their and specifically in the case of Apple the design of their products and the experience we have with them. tones of voice These ideas are all reflected in various definitions we find in the world, if we do a quick search. From : Wikipedia A is a name, term, design, symbol or any other feature that one seller’s good or service from those of .[…] Brands are used in business, marketing, and advertising for recognition and, importantly, to create and store value as brand equity for the object identified, to the benefit of the brand’s customers, its owners and shareholders. brand identifies as distinct other sellers Heavy on the visual and more surface-level features, according to Wikipedia a brand identifies one seller’s goods or services as distinct from those of other sellers. Although the creation of brand value is an interesting and very important aspect – fit for a separate article. What is brand identity? Related, but separate as a concept, “ ” also has various definitions flying about the internet and in conversation. What is brand identity? Brand identity offers a fairly useful definition of Brand Identity: Investopedia is the of a brand, such as color, design, and logo, that identify and distinguish the brand in consumers’ minds. Brand identity is distinct from brand image. The former corresponds to the intent behind the branding and the way a company does the following — all to cultivate a certain image in consumers’ minds Brand identity visible elements Here we see that the general approach to brand and brand identity are mostly visual and that they are always about what sets one organization or seller apart from the other. But how can we expand our understanding, vocabulary, and toolsets when it comes to managing successful brands? Wally Olins — The Brand Handbook I find “ ” by Wally Olins to be a very helpful starting point to understanding brands better. The book offers exactly the expansion of vocabulary and tools to get a much better grip on brands, brand identity and brand management. It was gifted to me by my friend and mentor Roel Stavorinus, Corporate Identity guru and one of the Netherlands’ first official register marketers, who was in turn inspired by Olins. The Brand Handbook The multi-award-winning (December 19th 1930–April 14th 2014) was one of the world’s most respected and experienced practitioners of corporate identity and branding. He co-founded Wolff Olins and Saffron Brand Consultants and served as their chairman. Wally Olins Olins advised many of the world’s leading organizations on identity, branding, communication and related matters including 3i, Akzo Nobel, Repsol, Q8, The Portuguese Tourist Board, BT, Renault, Volkswagen, Tata and Lloyd’s of London. He acted as an advisor both to McKinsey and Bain. The Brand Handbook and the idea behind the brand In his seminal “The Brand Handbook” Olins explains with concise penmanship what brands are, how to create them, how to make them work, and how to sustain them. At the core of the brand, he writes, are a clear identity and mission. Olins: “The fundamental idea behind the is that in everything the organization does, everything it owns, and everything it produces it should project . The most significant way in which this can be done is by making everything in and around the organization — its — and performance and, where this is appropriate, ” brand a clear idea of what it is and what its aims are products, environment, communication and behavior consistent in purpose in appearance too. Note how “appearance” comes last, here. The importance of purpose and consistency in branding Olins underlines the importance of working from the inside out when it comes to brand, purpose, and consistency: “Outward consistency of this kind will only be achieved, and for that matter is only appropriate if it is the manifestation of an inward consistency — a consistency of purpose. This consistency of purpose derives from the vision, or the core idea, and is almost always the base from which a successful branding program(me) can be developed. The . It is what the organization is about, what it stands for, what it believes in. All organizations are unique even if the products/services they make are more or less the same as those of their competitors. It is the company’s history, structure, strategy, the personalities who have created and driven it forward, its successes and its failures, that shape it and make it what it is.” core idea drives the organization The rightful place of the visual elements of a brand We are now starting to see the picture. are important, but they’re not at the core of what makes a brand. What is the correct placing in terms of importance, of the visual brand elements? Visual brand elements Firstly, what visual elements are we talking about? Visual elements can be construed as the visible and/or tangible things like colors, typefaces or fonts, taglines or slogans — the ‘look and feel’. This can also incorporate what a product or store smells like, or how a brand experience might sound — as in Gary Vaynerchuk’s “Sonic Branding”. According to Olins out of all the visual elements, the logo or symbol is the prime identifier for almost all brands, its purpose being to “present the core idea of the organization with impact, brevity and immediacy.” “The logo encapsulates the brand.” Together with the core idea, the visual elements mark out the brand territory. Expanding on these two core elements and clarifying the relation between them, Olins further introduces the four vectors through which a brand makes itself tangible. The four brand vectors In his “Brand Handbook” Olins describes the fundamental idea that there are four vectors through which a brand — as defined by its core idea and surface, visual elements — manifests itself. These four vectors are Product, Environment, Communication, and Behavior. — stands for the products/services the organization sells, how they look and feel, and what the User Experience is for these. Product — the physical and digital environment of the brand, how it “lays out its stall”. What does your store or your LinkedIn company page look like? Environment — how it tells people, every audience, about itself and what it’s doing — think, internal and external communications, storytelling, content strategy, copywriting and general tone of voice. Communication — how its people behave to each other and the world outside — think HR policy & processes, leadership and organizational culture, but also recruitment, sales professionals, marketers, and customer service representatives. Behavior The six elements of a successful brand At the core, as you can see the first and quintessential part or element of a brand is its core idea; , mission, and vision. your organization’s purpose The second element would be the visual brand, which is not a “loose” element but one that is ideally derived from the “core idea”, and at almost every step mixed in with the four vectors through which a brand makes itself tangible. You could add the visual brand as an added layer over the graph above, as a way to visualize its place as the second – or maybe, rather, sixth – element of a brand. Think about the colors and/or maybe a logo used in the design of a Product; the brick-and-mortar storefront or conversely the website (Environment); the taglines or slogans — but also colors, layouts, etc.) used consistently in e-mails or campaigns (Communication), and your company logo on the shirt of the customer service representative who just made your customer ‘s day (Behavior). The main goal is to keep finding ways to communicate the core idea of the brand in everything you do. And conversely, to check everything you do with the core idea of your company. I find that these two core elements and four vectors – for a total of six brand elements - make it infinitely easier to think and talk about brand and brand identity, because they help us do it in a structured way. They can also be used as a basis for brand strategy and they are the six elements that you need to at least think about when thinking about creating and managing a successful brand. How to manage a brand successfully Brand management is undoubtedly handled best with a strategic long-term plan, which would be an entire article – if not an entire book - in and of itself. In this article, we focused on the elements that are at the core of brand identity and that should be considered when talking or thinking about brand management. In a future article, we’ll share more in-depth information about managing the processes of creating a brand identity, brand architecture, and managing the evolution of a brand. If you’re interested in learning more, and if you want to see how we manage our own brand, follow Lytho on social media or subscribe to our newsletter. The right tools for managing your brand assets — DAM platforms Finally, when you have all of the elements to creating and managing a successful brand in place, along with a fitting strategy to do so, a tool for managing your brand — and most notably and visually your brand assets – can be very helpful. Especially for marketing teams who are collaborating remotely with each other, their internal and external marketing ecosystem and other internal and external stakeholders, a can add a lot of value. Applied strategically, you will be sure to get the most value out of your brand and the related assets by using a DAM system. Digital Asset Management platform A few things a Digital Asset Management system can help you achieve are: 1. Using one source for all content Instead of scattering your content over different tools, a DAM gathers all your marketing content in one place. 2. Creating your own designs With a DAM that incorporates ‘Create & Publich’ functionalities, everyone is a designer. Predefined templates make it easy to create advertorials, websites or brochures within your content hub – and always on-brand. 3. Saving up to 70% of your time Advanced search options and easier feedback processes within DAM systems such as allow you to spend time on what matters. Want to learn more about the benefits of a DAM system to your brand management efforts? Lytho To learn more about the added value of a DAM system for managing your brand, download our whitepaper “ Improve your Marketing Performance with DAM.” Previously published at https://insights.lytho.com/what-makes-a-brand-stand-out

How To Hit a Brand Management  Home Run: 6 Key Elements

BLEISTEIN v. DONALDSON LITHOGRAPHING CO. 239 Court Filing, retrieved on September 29, 2023 is part of . You can jump to any part in this filing . This is the table of links with all parts. HackerNoon’s Legal PDF Series here Case Number: No. 117 Plaintiff: Bleistein Defendant: Donaldson Lithographing Decided Date: February 2, 1903 Location: Supreme Court of the United States TABLE OF CONTENT Argument for Plaintiffs in Error Argument for Defendant in Error Opinion of the Court JUSTICES HARLAN and MCKENTNA, dissenting About HackerNoon Legal PDF Series: We bring you the most important technical and insightful public domain court case filings. This court case 2023-0409 retrieved on September 29, 2023, from is part of the public domain. The court-created documents are works of the federal government, and under copyright law, are automatically placed in the public domain and may be shared without legal restriction. tile.loc.gov

Bleistein v. Donaldson Lithographing Co.: A Legal Precedent for Copyrighting Commercial Speech 

Advancing the Detection of Ultralight Vector Dark Matter through Novel Analytical Strategies

Authors:
(1) Taha Laroussi, Laboratoire d’Hydrodynamique (LadHyX), CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France;
(2) Mojtaba Jarrahi, Universit´e Paris-Saclay, CNRS, FAST, 91405 Orsay, France;
(3) Gabriel Amselem, Laboratoire d’Hydrodynamique (LadHyX), CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France. Table of Links Abstract and Introduction Methods Results Model Discussion, Acknowledgements and References Supplementary Material II. METHODS A. Culture preparation C. reinhardtii strain CC-125 (Chlamydomonas Resource Center, University of Minnesota, MN, USA) were cultured on a solid medium prepared with TrisAcetate-Phosphate (Gibco™ TAP, ThermoFischer Scientific, France) and agar every 4 weeks, to keep the strain motile, responsive to light and prevent as much as possible the cells from sticking to the walls of the devices. For experiments, colonies of C. reinhardtii were picked from solid cultures and recultured in liquid TAP. The cultures were placed in an agitating incubator at 176 rpm, under a day/light cycle of 14h/10h with an illuminance of 60 µmol · m−2 · s −1 and at a fixed temperature of 22◦C. The cells reached maximum motile cell density within 3 days [16], after which a solution of swimming C. reinhardtii was obtained. Before being used for experiments, the cultures underwent a series of centrifugation steps. This enabled to concentrate the algal solution, get rid of low-motility and dead algae, and of cellular debris. First, 45 mL of the liquid culture were centrifuged at 1057g for 10 minutes. Then, 39 mL of the supernatant was removed, and the bottom 6 mL were centrifuged at 73g for 2 minutes. The supernatant, containing the motile cells, was kept and centrifuged again at 285g for 5 minutes. The amount of supernatant was adjusted to obtain the desired algae final concentration. B. Experimental setup An array of shallow cylindrical wells was made in polydimethylsiloxane (PDMS, Dow-Corning Sylgard 184), using standard soft lithography techniques [17]. The wells had a depth of 32 µm and diameters ranging from 200 µm to 500 µm. The PDMS was rendered hydrophilic by plasma cleaning. Then, a drop of ≈ 10 µL of the algal solution was deposited on the PDMS. The device was closed with a plasma-activated glass slide by applying gentle pressure. The trapped algae were observed under a Nikon TI microscope, using a 4x objective. Images were recorded at 10 fps with a CMOS camera (Hamamatsu ORCAFlash4.0 LT, Hamamatsu Photonics, France). A longpass red filter with a 645 nm cut-on wavelength (Newport RG645) was placed between the microscope’s light source and the microwells. A 3 mm blue LED with a wavelength λ = 470 nm and a light intensity of 7000 mcd (Plan`ete Leds, France) was placed on the microscope’s plate, approximately 2 cm away from the microfluidic chip, on the same plane. The LED operating voltage range was between 2.4 V and 3.2 V and its operating current was 20 mA. The light intensity was tuned by varying the applied voltage. An illustration of the setup is shown in Fig. 1. The algae concentration ϕ was determined in each well from images captured at the beginning of the experiments, before exposition to a light stimulus. Initially, the algae swam randomly and were distributed homogeneously in each well. They were identified by thresholding the images, and the total area they occupied in each well was determined. The concentration in algae was then defined as the fraction of surface area occupied by the algae in the well. C. Measuring the local light intensity We estimated the local light intensity inside a well using the number of photons reaching the sensor of the camera. First, we determined the camera offset value by blocking off all the light to the camera and taking a 16-bit image. The spatial average intensity in grey value of all the pixels in the image was the camera’s offset. Then, a 16-bit setup image of the sample was taken at the current experimental condition, with the light of the microscope turned off and the blue LED light on. The camera offset value was then subtracted from each pixel in the setup image. The grey values were first converted to number of electrons by dividing each pixel in the image by the conversion gain of the camera. The electrons were converted to photons by dividing the number of electrons from each pixel by the quantum efficiency (QE) of the sensor at λ = 470 nm. Last, the local light intensity inside a well was computed as the average number of photons within the well. This paper is available on arxiv under CC 4.0 license. Authors: (1) Taha Laroussi, Laboratoire d’Hydrodynamique (LadHyX), CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France; (2) Mojtaba Jarrahi, Universit´e Paris-Saclay, CNRS, FAST, 91405 Orsay, France; (3) Gabriel Amselem, Laboratoire d’Hydrodynamique (LadHyX), CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France. Authors: Authors: (1) Taha Laroussi, Laboratoire d’Hydrodynamique (LadHyX), CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France; (2) Mojtaba Jarrahi, Universit´e Paris-Saclay, CNRS, FAST, 91405 Orsay, France; (3) Gabriel Amselem, Laboratoire d’Hydrodynamique (LadHyX), CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France. Table of Links Abstract and Introduction Abstract and Introduction Methods Methods Results Results Model Model Discussion, Acknowledgements and References Discussion, Acknowledgements and References Supplementary Material Supplementary Material II. METHODS A. Culture preparation C. reinhardtii strain CC-125 (Chlamydomonas Resource Center, University of Minnesota, MN, USA) were cultured on a solid medium prepared with TrisAcetate-Phosphate (Gibco™ TAP, ThermoFischer Scientific, France) and agar every 4 weeks, to keep the strain motile, responsive to light and prevent as much as possible the cells from sticking to the walls of the devices. For experiments, colonies of C. reinhardtii were picked from solid cultures and recultured in liquid TAP. The cultures were placed in an agitating incubator at 176 rpm, under a day/light cycle of 14h/10h with an illuminance of 60 µmol · m−2 · s −1 and at a fixed temperature of 22◦C. The cells reached maximum motile cell density within 3 days [16], after which a solution of swimming C. reinhardtii was obtained. Before being used for experiments, the cultures underwent a series of centrifugation steps. This enabled to concentrate the algal solution, get rid of low-motility and dead algae, and of cellular debris. First, 45 mL of the liquid culture were centrifuged at 1057g for 10 minutes. Then, 39 mL of the supernatant was removed, and the bottom 6 mL were centrifuged at 73g for 2 minutes. The supernatant, containing the motile cells, was kept and centrifuged again at 285g for 5 minutes. The amount of supernatant was adjusted to obtain the desired algae final concentration. B. Experimental setup An array of shallow cylindrical wells was made in polydimethylsiloxane (PDMS, Dow-Corning Sylgard 184), using standard soft lithography techniques [17]. The wells had a depth of 32 µm and diameters ranging from 200 µm to 500 µm. The PDMS was rendered hydrophilic by plasma cleaning. Then, a drop of ≈ 10 µL of the algal solution was deposited on the PDMS. The device was closed with a plasma-activated glass slide by applying gentle pressure. The trapped algae were observed under a Nikon TI microscope, using a 4x objective. Images were recorded at 10 fps with a CMOS camera (Hamamatsu ORCAFlash4.0 LT, Hamamatsu Photonics, France). A longpass red filter with a 645 nm cut-on wavelength (Newport RG645) was placed between the microscope’s light source and the microwells. A 3 mm blue LED with a wavelength λ = 470 nm and a light intensity of 7000 mcd (Plan`ete Leds, France) was placed on the microscope’s plate, approximately 2 cm away from the microfluidic chip, on the same plane. The LED operating voltage range was between 2.4 V and 3.2 V and its operating current was 20 mA. The light intensity was tuned by varying the applied voltage. An illustration of the setup is shown in Fig. 1. The algae concentration ϕ was determined in each well from images captured at the beginning of the experiments, before exposition to a light stimulus. Initially, the algae swam randomly and were distributed homogeneously in each well. They were identified by thresholding the images, and the total area they occupied in each well was determined. The concentration in algae was then defined as the fraction of surface area occupied by the algae in the well. C. Measuring the local light intensity We estimated the local light intensity inside a well using the number of photons reaching the sensor of the camera. First, we determined the camera offset value by blocking off all the light to the camera and taking a 16-bit image. The spatial average intensity in grey value of all the pixels in the image was the camera’s offset. Then, a 16-bit setup image of the sample was taken at the current experimental condition, with the light of the microscope turned off and the blue LED light on. The camera offset value was then subtracted from each pixel in the setup image. The grey values were first converted to number of electrons by dividing each pixel in the image by the conversion gain of the camera. The electrons were converted to photons by dividing the number of electrons from each pixel by the quantum efficiency (QE) of the sensor at λ = 470 nm. Last, the local light intensity inside a well was computed as the average number of photons within the well. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Short-term Memory Effects in the Phototactic Behavior of Microalgae: Methods

Table of Links Abstract and 1. Introduction 2. Methods 2.1. Modeling Panspermia and Terraformation 2.2. Identifying the Presence of Terraformed Planets and 2.3. Software and Availability 3. Results 3.1. Panspermia can increase the correlation between planets’ compositions and positions 3.2. Likely terraformed planets can be identified from clustering 4. Summary and Discussion 5. Acknowledgements and References APPENDIX A. Appendix 2.1. Modeling Panspermia and Terraformation We created an agent-based model to simulate life[2] spreading between planets orbiting different host stars. The model is initialized with 1000 planets (1 of which is terraformed/panspermia-capable), fixed in a frame of reference, and uniformly randomly distributed in a continuous 3D volume. All planets are assumed to be in different star systems (i.e., we assume one planet per star). “Planets” have compositions representing the observable characteristics of the planet, and “life” agents have compositions representing the observable characteristics of the planet which the life originates from. During simulation, terraformed planets [3] emit life towards a target non-terraformed planet at a constant velocity [4]. The target planets are selected based on proximity in position and in composition (see Sec. 2.1.4). When life arrives at a planet, the planet’s composition is modified (terraformed) based on both the initial composition of the planet and the composition of the incoming life. Life originating from that terraformed planet will then reflect its new composition. We assume that the time required for terraformation is negligible compared to the time required to travel between planets. Terraformed planets emit life at a fixed rate, provided suitable target planets exist (see Sec. 2.1.4). The simulation ends when all planets are terraformed, or no suitable target planets remain (Fig. 1B). 2.1.2. Compositions and Terraformation Both “life” and “planets” have compositions represented by vectors of 10 real numbers (each element ∈ [0, 1]). In our model, these compositions are abstractions, used as a means to compare the compatibility of any given life and planet. While we might in the abstract think of one vector representing the observable characteristics of a planet, this same vector would not represent the same observable characteristics of life compatible with that planet. For life, it instead represents the kind of planetary observable characteristics which are compatible with that life. For example, perhaps a planet’s composition vector V corresponds to an atmosphere composed of 95% CO2 and 5% N2. The same composition vector V in the context of life is used to refer to a kind of life which could be compatible with a planet with an atmospheric composition of 95% CO2 and 5% N2. This does not mean that life on such a planet is literally composed of 95% CO2 and 5% N2. This captures the idea that if a life and a planet have identical composition vectors, then that life will surely be able to terraform the planet[5]. Correspondingly, a life’s composition is identical to the planet from which it emits. Depending on the simulation parameters, initial compositions of each planet are randomly drawn from a uniform distribution. This is a loose approximation of the unknowns surrounding the distribution of diversity of planets between planetary systems (Tasker et al. 2020; Pacetti et al. 2022). Planet compositions are modified by the process of terraformation, where a mixing function determines how to generate the terraformed composition based on the non-terraformed planet composition and the incoming life’s composition. We apply a mixing function inspired by horizontal gene transfer, but other mixing functions could also be used. The most important feature we aim to capture is the bi-directional feedback between the terraforming life, and the terraformed planet—such that future life emitted from the terraformed planet will inherit the post-terraformation characteristics of that planet. We keep n = 1 randomly chosen element from the planet’s pre-terraformed composition, and the rest of the terraformed composition is inherited from the terraforming life (Fig. 1C). 2.1.3. Model Stepping 2.1.4. Target Planet Selection The destination selection aims to balance the need of identifying a target planet that is both compositionally similar, and physically near, the parent planet. This is based on the assumption that life directing panspermia would want to minimize travel time and terraformation energy costs. In the context of lithopanspermia, this could be interpreted as an assumption that beyond a certain positional distance capture becomes vanishingly unlikely, and beyond a certain compositional distance compatibility becomes vanishingly unlikely. Authors:
(1) Harrison B. Smith, Earth-Life Science Institute, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, Japan, and Blue Marble Space Institute of Science, Seattle, Washington, USA (hbs@elsi.jp);
(2) Lana Sinapayen, Sony Computer Science Laboratories, Kyoto, Japan and National Institute for Basic Biology, Okazaki, Japan (lana.sinapayen@gmail.com). This paper is available on arxiv under CC BY-NC-ND 4.0 Deed license. [2] In this work, we use life specifically to refer to an agent (used strictly in the “entity” sense of the word agent) traveling from a parent terraformed planet to a target non-terraformed planet, and whose arrival at the target planet triggers terraformation. [3] We specifically avoid saying living planets, because our methodology cannot distinguish between living planets incapable of panspermia and non-living planets. [4] This approach is most similar to directed panspermia by intelligent life, but could also be envisioned as undirected lithopanspermia, where we refrain from burdening the simulations with agents that won’t ever be able to interact with planets under the rules of our model. [5] This is an extreme example where technically life wouldn’t even need to terraform the planet, because it implies that the planet’s observable characteristics already perfectly match the planet from where the life originated. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Methods 2.1. Modeling Panspermia and Terraformation 2.1. Modeling Panspermia and Terraformation 2.2. Identifying the Presence of Terraformed Planets and 2.3. Software and Availability 2.2. Identifying the Presence of Terraformed Planets and 2.3. Software and Availability 3. Results 3.1. Panspermia can increase the correlation between planets’ compositions and positions 3.1. Panspermia can increase the correlation between planets’ compositions and positions 3.2. Likely terraformed planets can be identified from clustering 3.2. Likely terraformed planets can be identified from clustering 4. Summary and Discussion 4. Summary and Discussion 5. Acknowledgements and References 5. Acknowledgements and References APPENDIX APPENDIX A. Appendix A. Appendix 2.1. Modeling Panspermia and Terraformation We created an agent-based model to simulate life[2] spreading between planets orbiting different host stars. The model is initialized with 1000 planets (1 of which is terraformed/panspermia-capable), fixed in a frame of reference, and uniformly randomly distributed in a continuous 3D volume. All planets are assumed to be in different star systems (i.e., we assume one planet per star). “Planets” have compositions representing the observable characteristics of the planet, and “life” agents have compositions representing the observable characteristics of the planet which the life originates from. During simulation, terraformed planets [3] emit life towards a target non-terraformed planet at a constant velocity [4]. The target planets are selected based on proximity in position and in composition (see Sec. 2.1.4). When life arrives at a planet, the planet’s composition is modified (terraformed) based on both the initial composition of the planet and the composition of the incoming life. Life originating from that terraformed planet will then reflect its new composition. We assume that the time required for terraformation is negligible compared to the time required to travel between planets. Terraformed planets emit life at a fixed rate, provided suitable target planets exist (see Sec. 2.1.4). The simulation ends when all planets are terraformed, or no suitable target planets remain (Fig. 1B). 2.1.2. Compositions and Terraformation 2.1.2. Compositions and Terraformation Both “life” and “planets” have compositions represented by vectors of 10 real numbers (each element ∈ [0, 1]). In our model, these compositions are abstractions, used as a means to compare the compatibility of any given life and planet. While we might in the abstract think of one vector representing the observable characteristics of a planet, this same vector would not represent the same observable characteristics of life compatible with that planet. For life, it instead represents the kind of planetary observable characteristics which are compatible with that life. For example, perhaps a planet’s composition vector V corresponds to an atmosphere composed of 95% CO2 and 5% N2. The same composition vector V in the context of life is used to refer to a kind of life which could be compatible with a planet with an atmospheric composition of 95% CO2 and 5% N2. This does not mean that life on such a planet is literally composed of 95% CO2 and 5% N2. This captures the idea that if a life and a planet have identical composition vectors, then that life will surely be able to terraform the planet[5]. Correspondingly, a life’s composition is identical to the planet from which it emits. Depending on the simulation parameters, initial compositions of each planet are randomly drawn from a uniform distribution. This is a loose approximation of the unknowns surrounding the distribution of diversity of planets between planetary systems (Tasker et al. 2020; Pacetti et al. 2022). Planet compositions are modified by the process of terraformation, where a mixing function determines how to generate the terraformed composition based on the non-terraformed planet composition and the incoming life’s composition. We apply a mixing function inspired by horizontal gene transfer, but other mixing functions could also be used. The most important feature we aim to capture is the bi-directional feedback between the terraforming life, and the terraformed planet—such that future life emitted from the terraformed planet will inherit the post-terraformation characteristics of that planet. We keep n = 1 randomly chosen element from the planet’s pre-terraformed composition, and the rest of the terraformed composition is inherited from the terraforming life (Fig. 1C). 2.1.3. Model Stepping 2.1.3. Model Stepping 2.1.4. Target Planet Selection 2.1.4. Target Planet Selection The destination selection aims to balance the need of identifying a target planet that is both compositionally similar, and physically near, the parent planet. This is based on the assumption that life directing panspermia would want to minimize travel time and terraformation energy costs. In the context of lithopanspermia, this could be interpreted as an assumption that beyond a certain positional distance capture becomes vanishingly unlikely, and beyond a certain compositional distance compatibility becomes vanishingly unlikely. Authors: (1) Harrison B. Smith, Earth-Life Science Institute, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, Japan, and Blue Marble Space Institute of Science, Seattle, Washington, USA (hbs@elsi.jp); (2) Lana Sinapayen, Sony Computer Science Laboratories, Kyoto, Japan and National Institute for Basic Biology, Okazaki, Japan (lana.sinapayen@gmail.com). Authors: Authors: (1) Harrison B. Smith, Earth-Life Science Institute, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, Japan, and Blue Marble Space Institute of Science, Seattle, Washington, USA ( hbs@elsi.jp ); hbs@elsi.jp (2) Lana Sinapayen, Sony Computer Science Laboratories, Kyoto, Japan and National Institute for Basic Biology, Okazaki, Japan ( lana.sinapayen@gmail.com ). lana.sinapayen@gmail.com This paper is available on arxiv under CC BY-NC-ND 4.0 Deed license. This paper is available on arxiv under CC BY-NC-ND 4.0 Deed license. available on arxiv [2] In this work, we use life specifically to refer to an agent (used strictly in the “entity” sense of the word agent) traveling from a parent terraformed planet to a target non-terraformed planet, and whose arrival at the target planet triggers terraformation. [3] We specifically avoid saying living planets, because our methodology cannot distinguish between living planets incapable of panspermia and non-living planets. [4] This approach is most similar to directed panspermia by intelligent life, but could also be envisioned as undirected lithopanspermia, where we refrain from burdening the simulations with agents that won’t ever be able to interact with planets under the rules of our model. [5] This is an extreme example where technically life wouldn’t even need to terraform the planet, because it implies that the planet’s observable characteristics already perfectly match the planet from where the life originated.

A Biosignature Based on Modeling Panspermia and Terraformation: Modeling

Authors:
(1) Harrison B. Smith, Earth-Life Science Institute, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, Japan, and Blue Marble Space Institute of Science, Seattle, Washington, USA (hbs@elsi.jp);
(2) Lana Sinapayen, Sony Computer Science Laboratories, Kyoto, Japan and National Institute for Basic Biology, Okazaki, Japan (lana.sinapayen@gmail.com). Table of Links Abstract and 1. Introduction 2. Methods 2.1. Modeling Panspermia and Terraformation 2.2. Identifying the Presence of Terraformed Planets and 2.3. Software and Availability 3. Results 3.1. Panspermia can increase the correlation between planets’ compositions and positions 3.2. Likely terraformed planets can be identified from clustering 4. Summary and Discussion 5. Acknowledgements and References APPENDIX A. Appendix ABSTRACT A fundamental goal of astrobiology is to detect life outside of Earth. This proves to be an exceptional challenge outside of our solar system, where strong assumptions must be made about how life would manifest and interact with its planet. Such assumptions are required because of the lack of a consensus theory of living systems, or an understanding of the possible extent of planetary dynamics. Here we explore a model of life spreading between planetary systems via panspermia and terraformation. Our model shows that as life propagates across the galaxy, correlations emerge between planetary characteristics and location, and can function as a population-scale agnostic biosignature. This biosignature is agnostic because it is independent of strong assumptions about any particular instantiation of life or planetary characteristic—by focusing on a specific hypothesis of what life may do, rather than what life may be. By clustering planets based on their observed characteristics, and examining the spatial extent of these clusters, we demonstrate (and evaluate) a way to prioritize specific planets for further observation—based on their potential for containing life. We consider obstacles that must be overcome to practically implement our approach, including identifying specific ways in which better understanding astrophysical and planetary processes would improve our ability to detect life. Finally, we consider how this model leads us to think in novel ways about hierarchies of life and planetary scale replication. 1. INTRODUCTION It is difficult to attribute, with certainty, observable features of exoplanets to extraterrestrial life (Moore et al. 2017; Tasker et al. 2017; Green et al. 2021; Cockell 2022; Lenardic et al. 2022, 2023; Smith & Mathis 2023). This is exemplified by the insufficient (and often ill-defined) working definitions of life that are used to interpret observational data, and by the growing number of false positives for traditional biosignatures (Cleland & Chyba 2002; Benner 2010; Cleland 2012; Mix 2015; Schwieterman et al. 2016; Bich & Green 2018; Harman & Domagal-Goldman 2018; Schwieterman et al. 2018; Mariscal & Doolittle 2020; Janin 2021; Vickers et al. 2023). One way in which the community aims to overcome the problems with defining life is to develop “agnostic” biosignatures—detecting signs of life that are not particular to Earth-life or any other hypothetical instances of life (Marshall et al. 2021; Smith et al. 2021). Yet, agnostic biosignature proposals are sometimes built on restricted concepts of habitability (e.g., requiring rocky, watery planets), or simple anomaly detection (i.e., without using a working definition of life) (Kinney & Kempes 2022; Cleaves et al. 2023). A proposed remedy for the issues surrounding traditional biosignatures has been to use so-called “statistical” biosignatures—relying on integrating multiple lines of evidence to increase confidence in a discovery, or generating ensembles of data to better constrain the probabilities P(data|abiotic) and P(data|life) (in Bayesian speak). (Lin & Loeb 2015; Catling et al. 2018; Walker et al. 2018; Affholder et al. 2021; Bixel & Apai 2021). However, such statistical biosignatures often rely on assumptions about the prior probability of abiogenesis, or on the existence of unambiguous biosignatures for single planets. These approaches are often trying to solve more specific issues, like estimating the frequency of Earth-like life, the frequency of planets originating from panspermia compared to abiogenesis, or finding evidence of a specific metabolic process (Lin & Loeb 2015; Walker et al. 2018; Affholder et al. 2021; Checlair et al. 2021; Kovacevic 2022). Here we ask, can we detect the presence of life if we postulate that life is spreading between and terraforming planets?[1] This is an astrobiological “hinge proposition” of the kind described by Kinney & Kempes as necessary to make sure “that the door of astrobiology can turn properly” under conditions of deep uncertainty (Kinney & Kempes 2022). It is also somewhat the converse of a question posed in other panspermia related work: Can the prevalence of panspermia be constrained when assuming we have a way to detect life? (Lin & Loeb 2015; Balbi & Grimaldi 2020; Grimaldi et al. 2021; Lingam et al. 2021; Kovacevic 2022). In fact, our postulates (of terraformation and panspermia) are less peculiar than they might at first seem: while existing work doesn’t always explicitly refer to terraformation, it must be assumed—in the sense that the mere presence of life stable at geological timescales would create environmental feedback with a planet, and if that life is to be detectable it must modify a planet’s observables. Such planetary modification by life is a well documented phenomena—e.g., the rise of O2 during the great oxygenation event (Lynas et al. 2021), or the rise of CO2 from human industrial activity (Olejarz et al. 2021)). The feasibility of interstellar lithopanspermia (nonintelligent exchange of material via rocks) has been discussed at length in other work (see e.g. CarrollNellenback et al. (2019); Grimaldi et al. (2021); Gobat (2021); Totani (2023) and references therein). Crucially, it appears plausible, although likelihoods and rates vary considerably depending on assumptions on timing, amount of material ejected, organismal hardiness, and capture rates, among other features. Arguments have likewise been made for the feasibility of directed interstellar panspermia by intelligent life (Wright et al. 2014). Ultimately, our postulates of panspermia and terraformation are merely well understood hallmarks of life (proliferation via replication, and adaptation with bi-directional environmental feedback), escalated to the planetary scale, and executed on an interstellar scale. We use a simulated model to show that statistical correlations between the spatial distribution of planets around different host stars, and their observable characteristics would itself be evidence of life, without the need for a separate biosignature that could reliably detect life on any given planet in isolation. The agnosticism of this biosignature is inseparable from its emergence at the scale of a population of planets—singleton planetary anomalies might be explained away by unknown geochemical processes, or targeted simply because they are anomalous (without a clear hypothesis of why they should be explained by life). Hypothesizing that life spreads via panspermia and terraformation allows us to search for biosignatures while forgoing any strong assumptions about not only the peculiarities of life (e.g., its metabolism) and planetary habitability (e.g., requiring surface liquid water) (Gobat 2021), but even the potential breadth of structure and chemical complexity underpinning living systems (Sol´e & Munteanu 2004; Kim et al. 2019; Bartlett et al. 2022; Wong et al. 2023). We first describe our model (Sec. 2.1) and approach for statistically identifying the presence of terraformed planets (Sec. 2.2). We show that evolving our model in time can increase the correlation between planets’ compositions and positions (Sec. 3.1). To identify specific planets likely to have been terraformed, we cluster planets by observable characteristics, then select clusters which are spatially localized and cause a decrease in correlation when removed (Secs. 2.2.3, 2.2.4 ). We evaluate these clusters by calculating how well they correctly classify terraformed planets as being terraformed, and non-terraformed planets as being non-terraformed (Sec. 3.2). Finally, we discuss how our results might change due to theoretical and observational constraints, identify specific ways in which better understanding astrophysical and planetary processes could improve life detection, and speculate on the concept of life at the scale of populations of planets. This paper is available on arxiv under CC BY-NC-ND 4.0 Deed license. [1] Here, “life spreading” refers to interstellar panspermia, and “terraforming planets” refers to modifying observable characteristics of planets. Authors: (1) Harrison B. Smith, Earth-Life Science Institute, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, Japan, and Blue Marble Space Institute of Science, Seattle, Washington, USA (hbs@elsi.jp); (2) Lana Sinapayen, Sony Computer Science Laboratories, Kyoto, Japan and National Institute for Basic Biology, Okazaki, Japan (lana.sinapayen@gmail.com). Authors: Authors: (1) Harrison B. Smith, Earth-Life Science Institute, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, Japan, and Blue Marble Space Institute of Science, Seattle, Washington, USA ( hbs@elsi.jp ); hbs@elsi.jp (2) Lana Sinapayen, Sony Computer Science Laboratories, Kyoto, Japan and National Institute for Basic Biology, Okazaki, Japan ( lana.sinapayen@gmail.com ). lana.sinapayen@gmail.com Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Methods 2.1. Modeling Panspermia and Terraformation 2.1. Modeling Panspermia and Terraformation 2.2. Identifying the Presence of Terraformed Planets and 2.3. Software and Availability 2.2. Identifying the Presence of Terraformed Planets and 2.3. Software and Availability 3. Results 3.1. Panspermia can increase the correlation between planets’ compositions and positions 3.1. Panspermia can increase the correlation between planets’ compositions and positions 3.2. Likely terraformed planets can be identified from clustering 3.2. Likely terraformed planets can be identified from clustering 4. Summary and Discussion 4. Summary and Discussion 5. Acknowledgements and References 5. Acknowledgements and References APPENDIX APPENDIX A. Appendix A. Appendix ABSTRACT A fundamental goal of astrobiology is to detect life outside of Earth. This proves to be an exceptional challenge outside of our solar system, where strong assumptions must be made about how life would manifest and interact with its planet. Such assumptions are required because of the lack of a consensus theory of living systems, or an understanding of the possible extent of planetary dynamics. Here we explore a model of life spreading between planetary systems via panspermia and terraformation. Our model shows that as life propagates across the galaxy, correlations emerge between planetary characteristics and location, and can function as a population-scale agnostic biosignature. This biosignature is agnostic because it is independent of strong assumptions about any particular instantiation of life or planetary characteristic—by focusing on a specific hypothesis of what life may do, rather than what life may be. By clustering planets based on their observed characteristics, and examining the spatial extent of these clusters, we demonstrate (and evaluate) a way to prioritize specific planets for further observation—based on their potential for containing life. We consider obstacles that must be overcome to practically implement our approach, including identifying specific ways in which better understanding astrophysical and planetary processes would improve our ability to detect life. Finally, we consider how this model leads us to think in novel ways about hierarchies of life and planetary scale replication. 1. INTRODUCTION It is difficult to attribute, with certainty, observable features of exoplanets to extraterrestrial life (Moore et al. 2017; Tasker et al. 2017; Green et al. 2021; Cockell 2022; Lenardic et al. 2022, 2023; Smith & Mathis 2023). This is exemplified by the insufficient (and often ill-defined) working definitions of life that are used to interpret observational data, and by the growing number of false positives for traditional biosignatures (Cleland & Chyba 2002; Benner 2010; Cleland 2012; Mix 2015; Schwieterman et al. 2016; Bich & Green 2018; Harman & Domagal-Goldman 2018; Schwieterman et al. 2018; Mariscal & Doolittle 2020; Janin 2021; Vickers et al. 2023). One way in which the community aims to overcome the problems with defining life is to develop “agnostic” biosignatures—detecting signs of life that are not particular to Earth-life or any other hypothetical instances of life (Marshall et al. 2021; Smith et al. 2021). Yet, agnostic biosignature proposals are sometimes built on restricted concepts of habitability (e.g., requiring rocky, watery planets), or simple anomaly detection (i.e., without using a working definition of life) (Kinney & Kempes 2022; Cleaves et al. 2023). A proposed remedy for the issues surrounding traditional biosignatures has been to use so-called “statistical” biosignatures—relying on integrating multiple lines of evidence to increase confidence in a discovery, or generating ensembles of data to better constrain the probabilities P(data|abiotic) and P(data|life) (in Bayesian speak). (Lin & Loeb 2015; Catling et al. 2018; Walker et al. 2018; Affholder et al. 2021; Bixel & Apai 2021). However, such statistical biosignatures often rely on assumptions about the prior probability of abiogenesis, or on the existence of unambiguous biosignatures for single planets. These approaches are often trying to solve more specific issues, like estimating the frequency of Earth-like life, the frequency of planets originating from panspermia compared to abiogenesis, or finding evidence of a specific metabolic process (Lin & Loeb 2015; Walker et al. 2018; Affholder et al. 2021; Checlair et al. 2021; Kovacevic 2022). Here we ask, can we detect the presence of life if we postulate that life is spreading between and terraforming planets?[1] This is an astrobiological “hinge proposition” of the kind described by Kinney & Kempes as necessary to make sure “that the door of astrobiology can turn properly” under conditions of deep uncertainty (Kinney & Kempes 2022). It is also somewhat the converse of a question posed in other panspermia related work: Can the prevalence of panspermia be constrained when assuming we have a way to detect life? (Lin & Loeb 2015; Balbi & Grimaldi 2020; Grimaldi et al. 2021; Lingam et al. 2021; Kovacevic 2022). In fact, our postulates (of terraformation and panspermia) are less peculiar than they might at first seem: while existing work doesn’t always explicitly refer to terraformation, it must be assumed—in the sense that the mere presence of life stable at geological timescales would create environmental feedback with a planet, and if that life is to be detectable it must modify a planet’s observables. Such planetary modification by life is a well documented phenomena—e.g., the rise of O2 during the great oxygenation event (Lynas et al. 2021), or the rise of CO2 from human industrial activity (Olejarz et al. 2021)). The feasibility of interstellar lithopanspermia (nonintelligent exchange of material via rocks) has been discussed at length in other work (see e.g. CarrollNellenback et al. (2019); Grimaldi et al. (2021); Gobat (2021); Totani (2023) and references therein). Crucially, it appears plausible, although likelihoods and rates vary considerably depending on assumptions on timing, amount of material ejected, organismal hardiness, and capture rates, among other features. Arguments have likewise been made for the feasibility of directed interstellar panspermia by intelligent life (Wright et al. 2014). Ultimately, our postulates of panspermia and terraformation are merely well understood hallmarks of life (proliferation via replication, and adaptation with bi-directional environmental feedback), escalated to the planetary scale, and executed on an interstellar scale. We use a simulated model to show that statistical correlations between the spatial distribution of planets around different host stars, and their observable characteristics would itself be evidence of life, without the need for a separate biosignature that could reliably detect life on any given planet in isolation. The agnosticism of this biosignature is inseparable from its emergence at the scale of a population of planets—singleton planetary anomalies might be explained away by unknown geochemical processes, or targeted simply because they are anomalous (without a clear hypothesis of why they should be explained by life). Hypothesizing that life spreads via panspermia and terraformation allows us to search for biosignatures while forgoing any strong assumptions about not only the peculiarities of life (e.g., its metabolism) and planetary habitability (e.g., requiring surface liquid water) (Gobat 2021), but even the potential breadth of structure and chemical complexity underpinning living systems (Sol´e & Munteanu 2004; Kim et al. 2019; Bartlett et al. 2022; Wong et al. 2023). We first describe our model (Sec. 2.1) and approach for statistically identifying the presence of terraformed planets (Sec. 2.2). We show that evolving our model in time can increase the correlation between planets’ compositions and positions (Sec. 3.1). To identify specific planets likely to have been terraformed, we cluster planets by observable characteristics, then select clusters which are spatially localized and cause a decrease in correlation when removed (Secs. 2.2.3, 2.2.4 ). We evaluate these clusters by calculating how well they correctly classify terraformed planets as being terraformed, and non-terraformed planets as being non-terraformed (Sec. 3.2). Finally, we discuss how our results might change due to theoretical and observational constraints, identify specific ways in which better understanding astrophysical and planetary processes could improve life detection, and speculate on the concept of life at the scale of populations of planets. This paper is available on arxiv under CC BY-NC-ND 4.0 Deed license. This paper is available on arxiv under CC BY-NC-ND 4.0 Deed license. available on arxiv [1] Here, “life spreading” refers to interstellar panspermia, and “terraforming planets” refers to modifying observable characteristics of planets.

A Biosignature Based on Modeling Panspermia and Terraformation: Abstract and Introduction

Authors:
(1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp);
(2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References 4 Conclusions and discussions We have investigated whether inflation in the early universe can be induced by an extra component of a 5d U(1) gauge field coupled to fermions in the RS warped spacetime or not. Imposing CBCs on fields involved in inflation, we have shown that the one-loop effective potential for a Wilson line phase obtained by quantum corrections can behave as an inflaton potential by finding parameter regions consistent with Planck 2018 results. Our model shares basic properties with higher-dimensional models on a flat spacetime, e.g., a potential is generated radiatively, and is robust owing to the gauge symmetry, and then a model has a predictability for physics on inflation. The remaining issues and future prospects are as follows. There is a fine-tuning problem that the (initial) vaules of φ and other parameters should be chosen in order to make φ as an inflaton work well. It would be better if they are determined from a fundamental theory. Or we would have to rely on the anthropic principle in the framework of multiverse. It is necessary to consider contributions of a radion and/or modulus in order to identify an inflaton. In concrete, it is essential to study their stabilization and how inflation can be realized in a system with such several scalar fields including a Wilson line phase on the RS warped background. It would be wonderful to construct a more realistic higher-dimensional gauge theory which solves riddles of particle physics and cosmology on a similar footing. More specifically, it would be fantastic that, in a system governed by the gauge principle, there are several Wilson line phases originated from extra components of gauge bosons, which behave as Higgs boson, an inflaton, a dark matter and so forth. A top-down approach would be useful to construct such a model in a more unified form. Superstring theory, for instance, provides many scalar and vector fields, and possesses many candidates of Higgs boson, an inflaton, a dark matter and so on. Hence, it is intriguing to investigate how a 5d effective theory on the warped geometry can be realized in such a top-down framework. Acknowledgements T.K. would like to thank Dr. O. Seto for the helpful discussions and advice. This work was supported in part by scientific grants from the Ministry of Education, Culture, Sports, Science and Technology under Grant No. 22K03632 (YK). References [1] D. H. Lyth and A. Riotto, “Particle physics models of inflation and the cosmological density perturbation”, Phys. Rept. 314 , 1 (1999), arXiv:hep-ph/9807278, and references therein. [2] Y. Hosotani, “Dynamical Mass Generation by Compact Extra Dimensions”, Phys. Lett. B126, 309 (1983). [3] Y. Hosotani, “Dynamics of Nonintegrable Phases and Gauge Symmetry Breaking”, Annals. Phys. 190, 233 (1989). [4] N. Arkani-Hamed, H.-C. Cheng, P. Creminelli, and L. Randall, “Extranatural Inflation”, Phys. Rev. Lett. 90, 221302 (2003), arXiv:hep-th/0301218. [5] Y. Abe, T. Inami, Y. Kawamura, and Y. Koyama, “Radion stabilization in the presence of a Wilson line phase”, Prog. Theor. Exp. Phys. 2014, 073B04 (2014), arXiv:1404.5125 [hep-th]. [6] Y. Abe, T. Inami, Y. Kawamura, and Y. Koyama, “Inflation from radion gauge-Higgs potential at Planck scale”, Prog. Theor. Exp. Phys. 2015, 093B03 (2015), arXiv:1504.06905 [hep-th]. [7] N. Aghanim et al. (Planck), “Planck 2018 results. VI. Cosmological parameters”, Astron. Astrophys. 641, [Erratum: Astron.Astrophys. 652, C4 (2021)], A6 (2020), arXiv:1807.06209 [astro-ph.CO]. [8] L. Randall and R. Sundrum, “A Large mass hierarchy from a small extra dimension”, Phys. Rev. Lett. 83, 3370-3373 (1999), arXiv:hep-ph/9905221. [9] L. Randall and R. Sundrum, “An Alternative to compactification”, Phys. Rev. Lett. 83, 4690-4693 (1999), arXiv:hep-ph/9906064. [10] A. D. Medina, N. R. Shah, and C. E. M. Wagner, “Gauge-Higgs Unification and Radiative Electroweak Symmetry Breaking in Warped Extra Dimensions”, Phys. Rev. D 76, 095010 (2007), arXiv:0706.1281 [hep-ph]. [11] Y. Hosotani, K. Oda, T. Ohnuma, and Y. Sakamura, “Dynamical Electroweak Symmetry Breaking in SO(5) × U(1) Gauge-Higgs Unification with Top and Bottom Quarks”, Phys. Rev. D 78, [Erratum: Phys. Rev.D 79, 079902 (2009)], 096002 (2008), arXiv:0806.0480[hep-ph]. [12] Y. Hosotani, “New dimensions from gauge-Higgs unification”, PoS CORFU2016, 026 (2017), arXiv:1702.08161 [hep-ph]. [13] S. Funatsu, H. Hatanaka, Y. Hosotani, Y. Orikasa, and N. Yamatsu, “CKM matrix and FCNC suppression in SO(5)×U(1)×SU(3) gauge-Higgs unification”, Phys. Rev. D 101, 055016 (2020), arXiv:1909.00190 [hep-ph]. [14] A. Hebecker and J. March-Russell, “The structure of GUT breaking by orbifolding”, Nucl. Phys. B 625, 128-150 (2002), arXiv:hep-ph/0107039. [15] N. Haba, Y. Kawamura, and K.-y. Oda, “Dynamical Rearrangement of Theta Parameter in Presence of Mixed Chern-Simons Term”, Phys. Rev. D 78, 085021 (2008), arXiv:0803.4380 [hep-ph]. [16] Y. Abe, Y. Goto, Y. Kawamura, and Y. Nishikawa, “Conjugate boundary condition, hidden particles, and gauge-Higgs inflation”, Mod. Phys. Lett. A 31, 1650208 (2016), arXiv:1608.06393 [hep-ph]. [17] K. Kojima and Y. Okubo, “Early dark energy from a higher-dimensional gauge theory”, Phys. Rev. D 106, 063540 (2022), arXiv:2205.13777 [astro-ph.CO]. [18] C. C´saki, S. Lombardo, and O. Telem, “TASI Lectures on Non-supersymmetric BSM Models”, Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics : Anticipating the Next Discoveries in Particle Physics (TASI 2016): Boulder, CO, USA, June 6-July 1, 2016 , edited by R. Essig and I. Low (WSP, 2018), 501-570, arXiv:1811.04279 [hep-ph]. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Authors: Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References 4 Conclusions and discussions, Acknowledgements, and References 4 Conclusions and discussions We have investigated whether inflation in the early universe can be induced by an extra component of a 5d U(1) gauge field coupled to fermions in the RS warped spacetime or not. Imposing CBCs on fields involved in inflation, we have shown that the one-loop effective potential for a Wilson line phase obtained by quantum corrections can behave as an inflaton potential by finding parameter regions consistent with Planck 2018 results. Our model shares basic properties with higher-dimensional models on a flat spacetime, e.g., a potential is generated radiatively, and is robust owing to the gauge symmetry, and then a model has a predictability for physics on inflation. The remaining issues and future prospects are as follows. There is a fine-tuning problem that the (initial) vaules of φ and other parameters should be chosen in order to make φ as an inflaton work well. It would be better if they are determined from a fundamental theory. Or we would have to rely on the anthropic principle in the framework of multiverse. It is necessary to consider contributions of a radion and/or modulus in order to identify an inflaton. In concrete, it is essential to study their stabilization and how inflation can be realized in a system with such several scalar fields including a Wilson line phase on the RS warped background. It would be wonderful to construct a more realistic higher-dimensional gauge theory which solves riddles of particle physics and cosmology on a similar footing. More specifically, it would be fantastic that, in a system governed by the gauge principle, there are several Wilson line phases originated from extra components of gauge bosons, which behave as Higgs boson, an inflaton, a dark matter and so forth. A top-down approach would be useful to construct such a model in a more unified form. Superstring theory, for instance, provides many scalar and vector fields, and possesses many candidates of Higgs boson, an inflaton, a dark matter and so on. Hence, it is intriguing to investigate how a 5d effective theory on the warped geometry can be realized in such a top-down framework. Acknowledgements T.K. would like to thank Dr. O. Seto for the helpful discussions and advice. This work was supported in part by scientific grants from the Ministry of Education, Culture, Sports, Science and Technology under Grant No. 22K03632 (YK). References [1] D. H. Lyth and A. Riotto, “Particle physics models of inflation and the cosmological density perturbation”, Phys. Rept. 314 , 1 (1999), arXiv:hep-ph/9807278, and references therein. [2] Y. Hosotani, “Dynamical Mass Generation by Compact Extra Dimensions”, Phys. Lett. B126, 309 (1983). [3] Y. Hosotani, “Dynamics of Nonintegrable Phases and Gauge Symmetry Breaking”, Annals. Phys. 190, 233 (1989). [4] N. Arkani-Hamed, H.-C. Cheng, P. Creminelli, and L. Randall, “Extranatural Inflation”, Phys. Rev. Lett. 90, 221302 (2003), arXiv:hep-th/0301218. [5] Y. Abe, T. Inami, Y. Kawamura, and Y. Koyama, “Radion stabilization in the presence of a Wilson line phase”, Prog. Theor. Exp. Phys. 2014, 073B04 (2014), arXiv:1404.5125 [hep-th]. [6] Y. Abe, T. Inami, Y. Kawamura, and Y. Koyama, “Inflation from radion gauge-Higgs potential at Planck scale”, Prog. Theor. Exp. Phys. 2015, 093B03 (2015), arXiv:1504.06905 [hep-th]. [7] N. Aghanim et al. (Planck), “Planck 2018 results. VI. Cosmological parameters”, Astron. Astrophys. 641, [Erratum: Astron.Astrophys. 652, C4 (2021)], A6 (2020), arXiv:1807.06209 [astro-ph.CO]. [8] L. Randall and R. Sundrum, “A Large mass hierarchy from a small extra dimension”, Phys. Rev. Lett. 83, 3370-3373 (1999), arXiv:hep-ph/9905221. [9] L. Randall and R. Sundrum, “An Alternative to compactification”, Phys. Rev. Lett. 83, 4690-4693 (1999), arXiv:hep-ph/9906064. [10] A. D. Medina, N. R. Shah, and C. E. M. Wagner, “Gauge-Higgs Unification and Radiative Electroweak Symmetry Breaking in Warped Extra Dimensions”, Phys. Rev. D 76, 095010 (2007), arXiv:0706.1281 [hep-ph]. [11] Y. Hosotani, K. Oda, T. Ohnuma, and Y. Sakamura, “Dynamical Electroweak Symmetry Breaking in SO(5) × U(1) Gauge-Higgs Unification with Top and Bottom Quarks”, Phys. Rev. D 78, [Erratum: Phys. Rev.D 79, 079902 (2009)], 096002 (2008), arXiv:0806.0480[hep-ph]. [12] Y. Hosotani, “New dimensions from gauge-Higgs unification”, PoS CORFU2016, 026 (2017), arXiv:1702.08161 [hep-ph]. [13] S. Funatsu, H. Hatanaka, Y. Hosotani, Y. Orikasa, and N. Yamatsu, “CKM matrix and FCNC suppression in SO(5)×U(1)×SU(3) gauge-Higgs unification”, Phys. Rev. D 101, 055016 (2020), arXiv:1909.00190 [hep-ph]. [14] A. Hebecker and J. March-Russell, “The structure of GUT breaking by orbifolding”, Nucl. Phys. B 625, 128-150 (2002), arXiv:hep-ph/0107039. [15] N. Haba, Y. Kawamura, and K.-y. Oda, “Dynamical Rearrangement of Theta Parameter in Presence of Mixed Chern-Simons Term”, Phys. Rev. D 78, 085021 (2008), arXiv:0803.4380 [hep-ph]. [16] Y. Abe, Y. Goto, Y. Kawamura, and Y. Nishikawa, “Conjugate boundary condition, hidden particles, and gauge-Higgs inflation”, Mod. Phys. Lett. A 31, 1650208 (2016), arXiv:1608.06393 [hep-ph]. [17] K. Kojima and Y. Okubo, “Early dark energy from a higher-dimensional gauge theory”, Phys. Rev. D 106, 063540 (2022), arXiv:2205.13777 [astro-ph.CO]. [18] C. C´saki, S. Lombardo, and O. Telem, “TASI Lectures on Non-supersymmetric BSM Models”, Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics : Anticipating the Next Discoveries in Particle Physics (TASI 2016): Boulder, CO, USA, June 6-July 1, 2016 , edited by R. Essig and I. Low (WSP, 2018), 501-570, arXiv:1811.04279 [hep-ph]. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Exploring Gauge-Higgs Inflation with Extra Dimensions: Conclusions, Acknowledgements, and References

The semiconductor chip tug-of-war between the US and China has chip companies scrambling to keep business going as usual. AI is ruling the tech world right now, as gadget makers and software giants integrate the tech into everything to enhance and empower their products. And this AI push has created an unprecedented demand for semiconductor chips. If you don’t know what semiconductor chips do, know that they’re in almost all your digital consumer products like mobile phones, smartphones, digital cameras, televisions, washing machines, refrigerators, and LED bulbs. And some of them are mighty powerful. For example, Apple’s M4 chip is a powerful Neural Engine, that can conduct 38 trillion operations per second, making it much better for AI tasks and enhancing features like Live Captions and Visual Look Up on the iPad Pro. Deemed Apple’s most powerful Neural Engine, it’s “a breathtaking 60x faster than the first Neural Engine in A11 Bionic.” When this is the kind of power a chip can generate, it’s no wonder that nations are getting involved in its market share. US Pushes to Expand its Chips The US has been aggressive about expanding its chipmaking. In April, under the Chips Act, the US government announced an award of up to $6.4 billion in grants to South Korea’s Samsung to expand its chip production in central Texas. Under pressure from the US to curb chip exports to China, countries like The Netherlands, Japan, and South Korea have also placed restrictions on their companies. Last June, The Netherlands’ government announced plans to restrict exports of semiconductor technology to protect national security. At the beginning of the year, the Deutch government rescinded an export license to halt the shipment of two older lithography machines to Chinese customers. Last year, Japan imposed export controls on advanced microchip technologies in China. China’s Chip Stature China manufactures semiconductors, but also consumes a lot of them, creating a snug ecosystem of chips. In 2020, the country purchased 53.7% of the world’s supply of chips to the tune of US$240 billion. The country controls the majority of the business of semiconductor companies. In 2022, Qualcomm earned 50% of its revenues from China, NVIDIA 26.3%. Dutch company ASML Holding NV recorded 14% of its sales in the country and Apple 24%. In response to US’ aggressive chip market tactics, China has started upping its chip-making game. In a bid to gain self-reliance in chips, China has been working on a US $143 billion+ support package for its semiconductor industry. As part of its effort to reduce dependence on foreign suppliers, in May, Reuters reported two Chinese chipmakers have started producing high bandwidth memory (HBM) semiconductors, which are used in AI chipsets. In fact, Chinese tech conglomerate Huawei’s latest high-end phone now sports more Chinese suppliers. This includes a new flash memory storage chip and an improved chip processor. Some Chinese universities and research institutes even got hold of Nvidia’s high-end AI chips via resellers, according to Reuters. US Companies Rebel Another reason China isn’t bogged down yet is that US tech companies aren’t ready to let China go as a business partner yet. According to reports, many companies, like Qualcomm, ASML, and Apple, are ready to skip the US’ grants for business with China, owing to the smooth business relationship they’ve enjoyed so far with Chinese companies. This is why US chip sanctions aren’t appealing much to tech giants in the US. While these governments scramble to restrict Chinese business, companies are following their own path. In March, amongst all the political hubbub, Intel was able to sell chips worth hundred of millions of dollars to Huawei. China’s commerce minister has been wooing ASML to assure of China’s reliability as a business partner. Huawei, along with Nokia and Ericsson, are among the companies contracted to build 5G networks in China, with Samsung and Qualcomm also looking to gain greater market share in the country. A Shift in Chip Sentiment As the pressure mounts, some companies are beginning to toe the line though. The current chip situation has been setting off alarm bells for US companies like Intel, which depend on chip technology in a major way. They say they’re getting antsy about semiconductor manufacturing becoming concentrated in a single geographical location and have started taking steps for the future. In 2022, Intel signed the purchase agreement to become a landowner in Magdeburg, Germany, a planned site for its European semiconductor manufacturing facility. The tech company also brought on Bechtel as its general contractor for Intel’s new Ohio site already under construction. Semiconductor manufacturing is especially vulnerable given that 80 percent of current capacity is concentrated in one small geographic region. Our strategy is the industry’s strategy: Diversify our footprint today to bolster the chip supply needed for tomorrow
Keyvan Esfarjani, Executive vice president and chief global operations officer at Intel Corporationnone “Semiconductor manufacturing is especially vulnerable given that 80 percent of current capacity is concentrated in one small geographic region. Our strategy is the industry’s strategy: Diversify our footprint today to bolster the chip supply needed for tomorrow,” Keyvan Esfarjani, Executive vice president and chief global operations officer at Intel Corporation, said in a statement. Other companies are chipping in. November, last year, Nvidia offered a new advanced chip in China that meets the export restriction rules. According to Reuters, the chip, called the A800, represents the first reported effort by a US semiconductor company to create advanced processors for China that follow the new rules. In December, Taiwanese chipmaker TSMC announced tripling its planned investment in its Arizona plant to US$40 billion. The news was one of the largest foreign investment news in US history, with President Joe Biden personally going down there to hail the project. Chips to Chiplets Meanwhile, chip technology continues to innovate with rising demand. Chip makers like Nvidia, Intel, and AMD are pushing up their semiconductor abilities. These companies have introduced chiplet technology, a cheaper way to pack small semiconductor groups. Interestingly, China is offering this tech as well. The battle for supremacy in the semiconductor chip market between the US and China not only showcases geopolitical rivalries but also highlights the intricate interplay of technology, business, and international relations shaping the future of this critical industry. Navanwita Sachdev, Editor, The Tech Panda The semiconductor chip tug-of-war between the US and China has chip companies scrambling to keep business going as usual. AI is ruling the tech world right now, as gadget makers and software giants integrate the tech into everything to enhance and empower their products. And this AI push has created an unprecedented demand for semiconductor chips. If you don’t know what semiconductor chips do, know that they’re in almost all your digital consumer products like mobile phones, smartphones, digital cameras, televisions, washing machines, refrigerators, and LED bulbs. And some of them are mighty powerful. For example, Apple’s M4 chip is a powerful Neural Engine, that can conduct 38 trillion operations per second, making it much better for AI tasks and enhancing features like Live Captions and Visual Look Up on the iPad Pro. Deemed Apple’s most powerful Neural Engine, it’s “a breathtaking 60x faster than the first Neural Engine in A11 Bionic.” Apple’s M4 chip When this is the kind of power a chip can generate, it’s no wonder that nations are getting involved in its market share. US Pushes to Expand its Chips US Pushes to Expand its Chips The US has been aggressive about expanding its chipmaking. In April, under the Chips Act, the US government announced an award of up to $6.4 billion in grants to South Korea’s Samsung to expand its chip production in central Texas. $6.4 billion in grants Samsung Under pressure from the US to curb chip exports to China, countries like The Netherlands, Japan, and South Korea have also placed restrictions on their companies. Last June, The Netherlands’ government announced plans to restrict exports of semiconductor technology to protect national security. At the beginning of the year, the Deutch government rescinded an export license to halt the shipment of two older lithography machines to Chinese customers. Last year, Japan imposed export controls on advanced microchip technologies in China. announced rescinded imposed China’s Chip Stature China’s Chip Stature China manufactures semiconductors, but also consumes a lot of them, creating a snug ecosystem of chips. In 2020, the country purchased 53.7% of the world’s supply of chips to the tune of US$240 billion. The country controls the majority of the business of semiconductor companies. In 2022, Qualcomm earned 50% of its revenues from China, NVIDIA 26.3%. Dutch company ASML Holding NV recorded 14% of its sales in the country and Apple 24%. 53.7% Qualcomm NVIDIA ASML In response to US’ aggressive chip market tactics, China has started upping its chip-making game. In a bid to gain self-reliance in chips, China has been working on a US $143 billion+ support package for its semiconductor industry. US $143 billion+ As part of its effort to reduce dependence on foreign suppliers, in May, Reuters reported two Chinese chipmakers have started producing high bandwidth memory (HBM) semiconductors, which are used in AI chipsets. Reuters reported In fact, Chinese tech conglomerate Huawei’s latest high-end phone now sports more Chinese suppliers . This includes a new flash memory storage chip and an improved chip processor. Some Chinese universities and research institutes even got hold of Nvidia’s high-end AI chips via resellers, according to Reuters . Huawei’s more Chinese suppliers according to Reuters Reuters US Companies Rebel US Companies Rebel Another reason China isn’t bogged down yet is that US tech companies aren’t ready to let China go as a business partner yet. According to reports , many companies, like Qualcomm, ASML, and Apple, are ready to skip the US’ grants for business with China, owing to the smooth business relationship they’ve enjoyed so far with Chinese companies. According to reports This is why US chip sanctions aren’t appealing much to tech giants in the US. While these governments scramble to restrict Chinese business, companies are following their own path. In March, amongst all the political hubbub, Intel was able to sell chips worth hundred of millions of dollars to Huawei. Intel was able to sell China’s commerce minister has been wooing ASML to assure of China’s reliability as a business partner. Huawei, along with Nokia and Ericsson , are among the companies contracted to build 5G networks in China, with Samsung and Qualcomm also looking to gain greater market share in the country. has been wooing Nokia Ericsson contracted to build A Shift in Chip Sentiment A Shift in Chip Sentiment As the pressure mounts, some companies are beginning to toe the line though. The current chip situation has been setting off alarm bells for US companies like Intel, which depend on chip technology in a major way. They say they’re getting antsy about semiconductor manufacturing becoming concentrated in a single geographical location and have started taking steps for the future. has been setting off alarm bells In 2022, Intel signed the purchase agreement to become a landowner in Magdeburg, Germany, a planned site for its European semiconductor manufacturing facility. The tech company also brought on Bechtel as its general contractor for Intel’s new Ohio site already under construction. signed Semiconductor manufacturing is especially vulnerable given that 80 percent of current capacity is concentrated in one small geographic region. Our strategy is the industry’s strategy: Diversify our footprint today to bolster the chip supply needed for tomorrow Keyvan Esfarjani, Executive vice president and chief global operations officer at Intel Corporationnone Semiconductor manufacturing is especially vulnerable given that 80 percent of current capacity is concentrated in one small geographic region. Our strategy is the industry’s strategy: Diversify our footprint today to bolster the chip supply needed for tomorrow Semiconductor manufacturing is especially vulnerable given that 80 percent of current capacity is concentrated in one small geographic region. Our strategy is the industry’s strategy: Diversify our footprint today to bolster the chip supply needed for tomorrow Semiconductor manufacturing is especially vulnerable given that 80 percent of current capacity is concentrated in one small geographic region. Our strategy is the industry’s strategy: Diversify our footprint today to bolster the chip supply needed for tomorrow Keyvan Esfarjani, Executive vice president and chief global operations officer at Intel Corporation none Keyvan Esfarjani, Executive vice president and chief global operations officer at Intel Corporation “Semiconductor manufacturing is especially vulnerable given that 80 percent of current capacity is concentrated in one small geographic region. Our strategy is the industry’s strategy: Diversify our footprint today to bolster the chip supply needed for tomorrow,” Keyvan Esfarjani, Executive vice president and chief global operations officer at Intel Corporation, said in a statement. Other companies are chipping in. November, last year, Nvidia offered a new advanced chip in China that meets the export restriction rules. According to Reuters , the chip, called the A800, represents the first reported effort by a US semiconductor company to create advanced processors for China that follow the new rules. According to Reuters Reuters In December, Taiwanese chipmaker TSMC announced tripling its planned investment in its Arizona plant to US$40 billion . The news was one of the largest foreign investment news in US history, with President Joe Biden personally going down there to hail the project. TSMC Arizona plant to US$40 billion Chips to Chiplets Chips to Chiplets Meanwhile, chip technology continues to innovate with rising demand. Chip makers like Nvidia, Intel, and AMD are pushing up their semiconductor abilities. These companies have introduced chiplet technology , a cheaper way to pack small semiconductor groups. Interestingly, China is offering this tech as well. chiplet technology China The battle for supremacy in the semiconductor chip market between the US and China not only showcases geopolitical rivalries but also highlights the intricate interplay of technology, business, and international relations shaping the future of this critical industry. Navanwita Sachdev, Editor, The Tech Panda Navanwita Sachdev, Editor, The Tech Panda Navanwita Sachdev, Navanwita Sachdev, Navanwita Sachdev, Editor, The Tech Panda

AI Boom Spurs US-China Chip Race

এআই বুম স্পার্স ইউএস-চীন চিপ রেস

KI-Boom beflügelt Chip-Wettlauf zwischen den USA und China

El auge de la IA estimula la carrera de chips entre Estados Unidos y China

AI Boom stimule la course aux puces entre les États-Unis et la Chine

एआई बूम ने अमेरिका-चीन चिप रेस को बढ़ावा दिया

AIブームが米中のチップ競争を刺激

AI 붐으로 미국-중국 칩 경쟁 촉진

AI Boom estimula corrida de chips EUA-China

Бум искусственного интеллекта стимулирует гонку чипов между США и Китаем

AI Boom ABD-Çin Çip Yarışını Destekliyor

AI Boom thúc đẩy cuộc đua chip Mỹ-Trung

人工智能热潮激发中美芯片竞赛

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto;
(2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto;
(3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London;
(4) DANIEL GRIN, Haverford College;
(5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. Table of Links Abstract and Intro
Methods
Phenomenology
Discussion and Future Work
Conclusion
Acknowledgments and References 2. METHODS In order to model the behavior of extreme axions, we modified axionCAMB to include an arbitrary field potential shape (in our case, a cosine of the form given in Equation 1), and reconfigured the code to sample the extreme starting angles necessary to probe these potentials. We also modified the effective sound speed of the axions after the onset of oscillations to reflect the growth in structure resulting from the tachyonic field dynamics. Lastly, we implemented a computationally-efficient ‘lookup table’ of the axion background fluid evolution in order to speed up the computation of the perturbation equations of motion. The details of implementing extreme axions into axionCAMB are presented below [2]. 2.1. Review of axionCAMB The numerical treatment of axions in axionCAMB is described in detail in Hlozek et al. ˇ (2015), but we review the dynamics of axions here in a potential-agnostic way in order to set up our discussion of modeling extreme axions. In theory, the best way of modeling the dynamics of axion dark matter is to model the behaviour of the field throughout all of cosmic history, and derive all cosmological parameters from those primary variables. However, since this field evolution includes periods of extremely rapid oscillations at late times, simulating this is computationally prohibitive and numerically unstable. Instead, the axion field is modeled directly at early times, but the code switches to a simplified fluid approximation at late times (Hlozek et al. ˇ 2015). This piecewise background evolution could then be called when solving the equations of motion for the fluid perturbations (axion density perturbation δa and axion heat flux u), allowing for efficient and stable computation of the final axion power spectrum. This method is discussed here, building on the discussion in Hu (1998) and Hlozek et al. ˇ (2015). axionCAMB runs through this early pre-oscillatory phase several times in order to determine the proper initial value of the axion field required to produce the desired final axion density, and the time at which it can safely switch back to the free particle CDM solution at late times. It then dynamically evolves these initial conditions (integrating the equation of motion for a field using a Runge-Kutta integrator, Runge 1895) until the field starts to oscillate, at which point it switches over to the known free-particle solution for DM evolution (Hlozek et al. ˇ 2015). This results in a new set of equations of motion for the axion perturbations after the onset of oscillations: The perturbation equations of motion in these two regimes can be used to calculate the evolution of the axion perturbations, and make predictions for cosmological observables such as the MPS or CMB. 2.2. Finely tuned initial conditions Restructuring the initial shooting methods to specify the field starting angle allows us to probe the effects of extreme starting angles in new ways. We can specify starting angles arbitrarily close to π, in order to see the effects of these extremely finely tuned angles on other observables. In addition, when performing MCMC analysis, having the starting angle as a free parameter allows us to impose arbitrary priors on this starting angle. We can use these priors to test the dependence of any constraints on the level of fine tuning of the axion starting angle. 2.3. Modeling the early-oscillatory effective axion sound speed To get a sense of the effects of the anharmonic potential on the axion fluid sound speed, we first solve the axion field perturbation equations of motion, This approximation of the fluid sound speed is shown in red in the lower subplot of Figure 2. In order to approximate the boost in the axion sound speed shown in the field equations without changing the late-time evolution of the perturbations, we modified the vanilla axion fluid sound speed to include a large negative spike just after the onset of oscillations. This negative triangular spike is shown in green in the lower subplot of Figure 2. The width and height of this spike were fit to match the approximate sound speed computed from the field perturbation solution. The width (C1) was fit to the delay in scale factor a between the onset of axion oscillations and the asymptotic sign change in the field solution sound speed. This numerical width was then approximated as a power law function of the scale factor k of the perturbation, depends linearly on the scale factor at the onset of oscillations, which in turn depends on the axion mass, fraction, and starting angle, The power spectrum results for this method can be compared to the literature, where other groups have used the exact field perturbation equations of motion to compute the matter power spectrum for extreme axions, such as Leong et al. (2019). In Figure 3 we can see the comparison in the matter power spectrum for both a vanilla axion and an extreme axion with a starting angle deviating from π by 0.2 degrees, and we find that they are in remarkably close agreement with Leong et al. (2019). However, this close agreement seems to hold best at z = 0, when these power spectra are computed, while the higher redshifts comparison may be more nuanced. Figure 2 suggests that while the exact field solution and the new approximate fluid solution agree at very late times, their evolution at early times are not fully equivalent, so more work may need to be done on this approximation in order to perform comparisons to high-redshift observables. 2.4. Using lookup tables for efficient modeling of field Extending the full field evolution so much later past the onset of oscillations requires far more computational resources than ending the field evolution as soon as oscillations begin. Greater numerical resolution, in both time and possible field potential scale, is also required to integrate these rapidly oscillating variables. With these increases to computational time, the new version of axionCAMB takes around seventy seconds to complete. While this may be feasible when computing a single power spectrum result, this is computationally intensive with which to run an MCMC analysis, which may require tens to hundreds of thousands of separate calls to axionCAMB. 2.5. Summary of changes to axionCAMB In order to model axions with extreme starting angles in a cosine field potential using the computationally efficient field formalism used in axionCAMB, we have introduced a number of modifications to axionCAMB which are explained above, but summarized here. • We replaced the quadratic approximation of the field potential with an arbitrary potential function, currently set to the canonical cosine potential. • We modified the effective axion fluid sound speed to reproduce the growth in structure seen in the exact field perturbation equations of motion. • We precomputed a lookup table for the axion background evolution which significantly reduced the runtime. The result is an accurate modeling of extreme axion background and perturbation evolution for an arbitrary axion mass, density, and starting angle that only takes ∼ 7 seconds to run. This powerful tool can shed new light on the behaviour and detectability of these extreme axion models, as discussed below. 2.6. Data: Ly-α forest estimates of the MPS [2] axionCAMB is in turn based on the cosmological Boltzmann code, CAMB (Lewis & Bridle 2002). [4] A logarithmic dependence for the background field can be derived analytically for the anharmonic corrections to the relic density (Lyth 1992). This paper is available on arxiv under CC 4.0 license. Authors: (1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London; (4) DANIEL GRIN, Haverford College; (5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London; (4) DANIEL GRIN, Haverford College; (5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. Table of Links Abstract and Intro Methods Phenomenology Discussion and Future Work Conclusion Acknowledgments and References Abstract and Intro Abstract and Intro Methods Methods Phenomenology Phenomenology Discussion and Future Work Discussion and Future Work Conclusion Conclusion Acknowledgments and References Acknowledgments and References 2. METHODS In order to model the behavior of extreme axions, we modified axionCAMB to include an arbitrary field potential shape (in our case, a cosine of the form given in Equation 1), and reconfigured the code to sample the extreme starting angles necessary to probe these potentials. We also modified the effective sound speed of the axions after the onset of oscillations to reflect the growth in structure resulting from the tachyonic field dynamics. Lastly, we implemented a computationally-efficient ‘lookup table’ of the axion background fluid evolution in order to speed up the computation of the perturbation equations of motion. The details of implementing extreme axions into axionCAMB are presented below [2]. 2.1. Review of axionCAMB The numerical treatment of axions in axionCAMB is described in detail in Hlozek et al. ˇ (2015), but we review the dynamics of axions here in a potential-agnostic way in order to set up our discussion of modeling extreme axions. In theory, the best way of modeling the dynamics of axion dark matter is to model the behaviour of the field throughout all of cosmic history, and derive all cosmological parameters from those primary variables. However, since this field evolution includes periods of extremely rapid oscillations at late times, simulating this is computationally prohibitive and numerically unstable. Instead, the axion field is modeled directly at early times, but the code switches to a simplified fluid approximation at late times (Hlozek et al. ˇ 2015). This piecewise background evolution could then be called when solving the equations of motion for the fluid perturbations (axion density perturbation δa and axion heat flux u), allowing for efficient and stable computation of the final axion power spectrum. This method is discussed here, building on the discussion in Hu (1998) and Hlozek et al. ˇ (2015). axionCAMB runs through this early pre-oscillatory phase several times in order to determine the proper initial value of the axion field required to produce the desired final axion density, and the time at which it can safely switch back to the free particle CDM solution at late times. It then dynamically evolves these initial conditions (integrating the equation of motion for a field using a Runge-Kutta integrator, Runge 1895) until the field starts to oscillate, at which point it switches over to the known free-particle solution for DM evolution (Hlozek et al. ˇ 2015). This results in a new set of equations of motion for the axion perturbations after the onset of oscillations: The perturbation equations of motion in these two regimes can be used to calculate the evolution of the axion perturbations, and make predictions for cosmological observables such as the MPS or CMB. 2.2. Finely tuned initial conditions Restructuring the initial shooting methods to specify the field starting angle allows us to probe the effects of extreme starting angles in new ways. We can specify starting angles arbitrarily close to π, in order to see the effects of these extremely finely tuned angles on other observables. In addition, when performing MCMC analysis, having the starting angle as a free parameter allows us to impose arbitrary priors on this starting angle. We can use these priors to test the dependence of any constraints on the level of fine tuning of the axion starting angle. 2.3. Modeling the early-oscillatory effective axion sound speed To get a sense of the effects of the anharmonic potential on the axion fluid sound speed, we first solve the axion field perturbation equations of motion, This approximation of the fluid sound speed is shown in red in the lower subplot of Figure 2. In order to approximate the boost in the axion sound speed shown in the field equations without changing the late-time evolution of the perturbations, we modified the vanilla axion fluid sound speed to include a large negative spike just after the onset of oscillations. This negative triangular spike is shown in green in the lower subplot of Figure 2. The width and height of this spike were fit to match the approximate sound speed computed from the field perturbation solution. The width (C1) was fit to the delay in scale factor a between the onset of axion oscillations and the asymptotic sign change in the field solution sound speed. This numerical width was then approximated as a power law function of the scale factor k of the perturbation, depends linearly on the scale factor at the onset of oscillations, which in turn depends on the axion mass, fraction, and starting angle, The power spectrum results for this method can be compared to the literature, where other groups have used the exact field perturbation equations of motion to compute the matter power spectrum for extreme axions, such as Leong et al. (2019). In Figure 3 we can see the comparison in the matter power spectrum for both a vanilla axion and an extreme axion with a starting angle deviating from π by 0.2 degrees, and we find that they are in remarkably close agreement with Leong et al. (2019). However, this close agreement seems to hold best at z = 0, when these power spectra are computed, while the higher redshifts comparison may be more nuanced. Figure 2 suggests that while the exact field solution and the new approximate fluid solution agree at very late times, their evolution at early times are not fully equivalent, so more work may need to be done on this approximation in order to perform comparisons to high-redshift observables. 2.4. Using lookup tables for efficient modeling of field Extending the full field evolution so much later past the onset of oscillations requires far more computational resources than ending the field evolution as soon as oscillations begin. Greater numerical resolution, in both time and possible field potential scale, is also required to integrate these rapidly oscillating variables. With these increases to computational time, the new version of axionCAMB takes around seventy seconds to complete. While this may be feasible when computing a single power spectrum result, this is computationally intensive with which to run an MCMC analysis, which may require tens to hundreds of thousands of separate calls to axionCAMB. 2.5. Summary of changes to axionCAMB In order to model axions with extreme starting angles in a cosine field potential using the computationally efficient field formalism used in axionCAMB, we have introduced a number of modifications to axionCAMB which are explained above, but summarized here. • We replaced the quadratic approximation of the field potential with an arbitrary potential function, currently set to the canonical cosine potential. • We modified the effective axion fluid sound speed to reproduce the growth in structure seen in the exact field perturbation equations of motion. • We precomputed a lookup table for the axion background evolution which significantly reduced the runtime. The result is an accurate modeling of extreme axion background and perturbation evolution for an arbitrary axion mass, density, and starting angle that only takes ∼ 7 seconds to run. This powerful tool can shed new light on the behaviour and detectability of these extreme axion models, as discussed below. 2.6. Data: Ly-α forest estimates of the MPS [2] axionCAMB is in turn based on the cosmological Boltzmann code, CAMB (Lewis & Bridle 2002). [4] A logarithmic dependence for the background field can be derived analytically for the anharmonic corrections to the relic density (Lyth 1992).

Extreme Axions Unveiled: A Novel Fluid Approach for Cosmological Modeling - Methods

চরম অক্ষরেখা উন্মোচন: মহাজাগতিক মডেলিংয়ের জন্য একটি অভিনব তরল পদ্ধতি - পদ্ধতি

Extreme Axionen enthüllt: Ein neuartiger Fluidansatz für die kosmologische Modellierung - Methoden

Se revelan los axiones extremos: un nuevo enfoque fluido para el modelado cosmológico - Métodos

Extreme Axions dévoilés : une nouvelle approche fluide pour la modélisation cosmologique - Méthodes

चरम एक्सियंस का अनावरण: ब्रह्माण्ड संबंधी मॉडलिंग के लिए एक नवीन द्रव दृष्टिकोण - विधियाँ

極限アクシオンの解明：宇宙論モデリングのための新しい流体アプローチ - 方法

Extreme Axions 공개: 우주론적 모델링을 위한 새로운 유체 접근 방식 - 방법

Extreme Axions revelados: uma nova abordagem de fluidos para modelagem cosmológica - métodos

Представлены экстремальные аксионы: новый жидкостный подход к космологическому моделированию - Методы

Extreme Axions Ortaya Çıktı: Kozmolojik Modelleme için Yeni Bir Akışkan Yaklaşımı - Yöntemler

Ra mắt các Axion cực đoan: Một phương pháp tiếp cận chất lỏng mới cho mô hình vũ trụ - Phương pháp

揭开极端轴子的面纱：一种用于宇宙学建模的新型流体方法 - 方法

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto;
(2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto;
(3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London;
(4) DANIEL GRIN, Haverford College;
(5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. Table of Links Abstract and Intro
Methods
Phenomenology
Discussion and Future Work
Conclusion
Acknowledgments and References 6. ACKNOWLEDGEMENTS We are grateful to Wayne Hu, Tzihong Chiueh, Asimina Arvanitaki, Alex Lague, and Rayne Liu for their helpful discussions and advice. The Dunlap Institute is funded through an endowment established by the David Dunlap family and the University of Toronto. The authors at the University of Toronto acknowledge that the land on which the University of Toronto is built is the traditional territory of the Haudenosaunee, and most recently, the territory of the Mississaugas of the New Credit First Nation. They are grateful to have the opportunity to work in the community, on this territory. Computations were performed on the Niagara supercomputer at the SciNet HPC Consortium. SciNet is funded by Innovation, Science and Economic Development Canada; the Digital Research Alliance of Canada; the Ontario Research Fund: Research Excellence; and the University of Toronto. HW would like to acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) Canadian Graduate Scholarships - Master’s and Canadian Graduate Scholarships - Doctoral programs. DJEM is supported by an Ernest Rutherford Fellowship from the Science and Technologies Facilities Council (Grant No. ST/T004037/1) and by a Leverhulme Trust Research Project (RPG-2022-145). RH acknowledges support from the NSERC. RH additionally acknowledges support from CIFAR, and the Azrieli and Alfred. P. Sloan Foundations. REFERENCES Abazajian, K., et al. 2022. https://arxiv.org/abs/2203.08024 Abbott, L. F., & Sikivie, P. 1983, Phys. Lett. B, 120, 133, doi: 10.1016/0370-2693(83)90638-X Adams, C. B., et al. 2022, in Snowmass 2021. https://arxiv.org/abs/2203.14923 Aghanim, N., et al. 2016, Astron. Astrophys., 594, A11, doi: 10.1051/0004-6361/201526926 Akaike, H. 1974, IEEE Transactions on Automatic Control, 19, 716, doi: 10.1109/TAC.1974.1100705 Amendola, L., & Barbieri, R. 2006, Phys. Lett. B, 642, 192, doi: 10.1016/j.physletb.2006.08.069 Amendola, L., et al. 2018, Living Rev. Rel., 21, 2, doi: 10.1007/s41114-017-0010-3 Arvanitaki, A., Dimopoulos, S., Dubovsky, S., Kaloper, N., & March-Russell, J. 2010, Phys. Rev. D, 81, 123530, doi: 10.1103/PhysRevD.81.123530 Arvanitaki, A., Dimopoulos, S., Galanis, M., et al. 2020, Phys. Rev. D, 101, 083014, doi: 10.1103/PhysRevD.101.083014 Cedeno, F. X. L., Gonz ˜ alez-Morales, A. X., & Ure ´ na-L ˜ opez, L. A. ´ 2017, Phys. Rev., D96, 061301, doi: 10.1103/PhysRevD.96.061301 Cembranos, J. A. R., Maroto, A. L., Nu´nez Jare ˜ no, S. J., & ˜ Villarrubia-Rojo, H. 2018, JHEP, 08, 073, doi: 10.1007/JHEP08(2018)073 Dentler, M., Marsh, D. J. E., Hlozek, R., et al. 2022, Mon. Not. ˇ Roy. Astron. Soc., 515, 5646, doi: 10.1093/mnras/stac1946 Dine, M., & Fischler, W. 1983, Phys. Lett. B, 120, 137, doi: 10.1016/0370-2693(83)90639-1 du Mas des Bourboux, H., Rich, J., Font-Ribera, A., et al. 2020, ApJ, 901, 153, doi: 10.3847/1538-4357/abb085 Duffy, L. D., & van Bibber, K. 2009, New J. Phys., 11, 105008, doi: 10.1088/1367-2630/11/10/105008 Dvorkin, C., et al. 2022, in Snowmass 2021. https://arxiv.org/abs/2203.07064 Grin, D., Amin, M. A., Gluscevic, V., et al. 2019. https://arxiv.org/abs/1904.09003 Hlozek, R., Grin, D., Marsh, D. J. E., & Ferreira, P. G. 2015, Phys. ˇ Rev. D, 91, 103512, doi: 10.1103/PhysRevD.91.103512 Hlozek, R., Marsh, D. J. E., & Grin, D. 2018, Mon. Not. Roy. ˇ Astron. Soc., 476, 3063, doi: 10.1093/mnras/sty271 Hlozek, R., Marsh, D. J. E., Grin, D., et al. 2017, Phys. Rev. D, 95, ˇ 123511, doi: 10.1103/PhysRevD.95.123511 Hu, W. 1998, Astrophys. J., 506, 485, doi: 10.1086/306274 Hu, W., Barkana, R., & Gruzinov, A. 2000, Phys. Rev. Lett., 85, 1158, doi: 10.1103/PhysRevLett.85.1158 Hwang, J.-c., & Noh, H. 2009, Phys. Lett. B, 680, 1, doi: 10.1016/j.physletb.2009.08.031 Irsiˇ c, V., Viel, M., Haehnelt, M. G., Bolton, J. S., & Becker, G. D. ˇ 2017a, Phys. Rev. Lett., 119, 031302, doi: 10.1103/PhysRevLett.119.031302 Irsiˇ c, V., et al. 2017b, Mon. Not. Roy. Astron. Soc., 466, 4332, ˇ doi: 10.1093/mnras/stw3372 Jaeckel, J., Mehta, V. M., & Witkowski, L. T. 2017, JCAP, 1701, 036, doi: 10.1088/1475-7516/2017/01/036 Kamionkowski, M., & Riess, A. G. 2022. https://arxiv.org/abs/2211.04492 Khlopov, M., Malomed, B. A., & Zeldovich, I. B. 1985, Mon. Not. Roy. Astron. Soc., 215, 575 Lague, A., Bond, J. R., Hlo ¨ zek, R., Marsh, D. J. E., & S ˇ oding, L. ¨ 2021, Mon. Not. Roy. Astron. Soc., 504, 2391, doi: 10.1093/mnras/stab601 Lee, A., Abitbol, M. H., Adachi, S., et al. 2019, in Bulletin of the American Astronomical Society, Vol. 51, 147, doi: 10.48550/arXiv.1907.08284 Leong, K.-H., Schive, H.-Y., Zhang, U.-H., & Chiueh, T. 2019, Mon. Not. Roy. Astron. Soc., 484, 4273, doi: 10.1093/mnras/stz271 Lewis, A., & Bridle, S. 2002, PhRvD, 66, 103511, doi: 10.1103/PhysRevD.66.103511 Lu, L., Sargent, W. L. W., Womble, D. S., & Takada-Hidai, M. 1996, Astrophys. J., 472, 509, doi: 10.1086/526756 Lyth, D. H. 1992, Phys. Rev. D, 45, 3394, doi: 10.1103/PhysRevD.45.3394 Mao, Y.-Y., et al. 2022. https://arxiv.org/abs/2203.07252 Marsh, D. J. E. 2016, Phys. Rept., 643, 1, doi: 10.1016/j.physrep.2016.06.005 Parashari, P., & Laha, R. 2023, Mon. Not. Roy. Astron. Soc., 526, L63, doi: 10.1093/mnrasl/slad107 Peccei, R. D., & Quinn, H. R. 1977, Phys. Rev. D, 16, 1791, doi: 10.1103/PhysRevD.16.1791 Poulin, V., Smith, T. L., & Karwal, T. 2023. https://arxiv.org/abs/2302.09032 Preskill, J., Wise, M. B., & Wilczek, F. 1983, Phys. Lett. B, 120, 127, doi: 10.1016/0370-2693(83)90637-8 Rogers, K. K., Hlozek, R., Lagu ˇ e, A., et al. 2023, JCAP, 06, 023, ¨ doi: 10.1088/1475-7516/2023/06/023 Rogers, K. K., & Peiris, H. V. 2021, Phys. Rev. Lett., 126, 071302, doi: 10.1103/PhysRevLett.126.071302 Runge, C. 1895, Mathematische Annalen, 46, 167. https://api.semanticscholar.org/CorpusID:119924854 Svrcek, P., & Witten, E. 2006, JHEP, 06, 051, doi: 10.1088/1126-6708/2006/06/051 Urena L ˜ opez, L. A. 2019. ´ https://arxiv.org/abs/1904.03318 Zhang, U.-H., & Chiueh, T. 2017a, Phys. Rev. D, 96, 063522, doi: 10.1103/PhysRevD.96.063522 —. 2017b, Phys. Rev., D96, 023507, doi: 10.1103/PhysRevD.96.023507 This paper is available on arxiv under CC 4.0 license. Authors: (1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London; (4) DANIEL GRIN, Haverford College; (5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London; (4) DANIEL GRIN, Haverford College; (5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. Table of Links Abstract and Intro Methods Phenomenology Discussion and Future Work Conclusion Acknowledgments and References Abstract and Intro Abstract and Intro Methods Methods Phenomenology Phenomenology Discussion and Future Work Discussion and Future Work Conclusion Conclusion Acknowledgments and References Acknowledgments and References 6. ACKNOWLEDGEMENTS We are grateful to Wayne Hu, Tzihong Chiueh, Asimina Arvanitaki, Alex Lague, and Rayne Liu for their helpful discussions and advice. The Dunlap Institute is funded through an endowment established by the David Dunlap family and the University of Toronto. The authors at the University of Toronto acknowledge that the land on which the University of Toronto is built is the traditional territory of the Haudenosaunee, and most recently, the territory of the Mississaugas of the New Credit First Nation. They are grateful to have the opportunity to work in the community, on this territory. Computations were performed on the Niagara supercomputer at the SciNet HPC Consortium. SciNet is funded by Innovation, Science and Economic Development Canada; the Digital Research Alliance of Canada; the Ontario Research Fund: Research Excellence; and the University of Toronto. HW would like to acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) Canadian Graduate Scholarships - Master’s and Canadian Graduate Scholarships - Doctoral programs. DJEM is supported by an Ernest Rutherford Fellowship from the Science and Technologies Facilities Council (Grant No. ST/T004037/1) and by a Leverhulme Trust Research Project (RPG-2022-145). RH acknowledges support from the NSERC. RH additionally acknowledges support from CIFAR, and the Azrieli and Alfred. P. Sloan Foundations. REFERENCES Abazajian, K., et al. 2022. https://arxiv.org/abs/2203.08024 Abbott, L. F., & Sikivie, P. 1983, Phys. Lett. B, 120, 133, doi: 10.1016/0370-2693(83)90638-X Adams, C. B., et al. 2022, in Snowmass 2021. https://arxiv.org/abs/2203.14923 Aghanim, N., et al. 2016, Astron. Astrophys., 594, A11, doi: 10.1051/0004-6361/201526926 Akaike, H. 1974, IEEE Transactions on Automatic Control, 19, 716, doi: 10.1109/TAC.1974.1100705 Amendola, L., & Barbieri, R. 2006, Phys. Lett. B, 642, 192, doi: 10.1016/j.physletb.2006.08.069 Amendola, L., et al. 2018, Living Rev. Rel., 21, 2, doi: 10.1007/s41114-017-0010-3 Arvanitaki, A., Dimopoulos, S., Dubovsky, S., Kaloper, N., & March-Russell, J. 2010, Phys. Rev. D, 81, 123530, doi: 10.1103/PhysRevD.81.123530 Arvanitaki, A., Dimopoulos, S., Galanis, M., et al. 2020, Phys. Rev. D, 101, 083014, doi: 10.1103/PhysRevD.101.083014 Cedeno, F. X. L., Gonz ˜ alez-Morales, A. X., & Ure ´ na-L ˜ opez, L. A. ´ 2017, Phys. Rev., D96, 061301, doi: 10.1103/PhysRevD.96.061301 Cembranos, J. A. R., Maroto, A. L., Nu´nez Jare ˜ no, S. J., & ˜ Villarrubia-Rojo, H. 2018, JHEP, 08, 073, doi: 10.1007/JHEP08(2018)073 Dentler, M., Marsh, D. J. E., Hlozek, R., et al. 2022, Mon. Not. ˇ Roy. Astron. Soc., 515, 5646, doi: 10.1093/mnras/stac1946 Dine, M., & Fischler, W. 1983, Phys. Lett. B, 120, 137, doi: 10.1016/0370-2693(83)90639-1 du Mas des Bourboux, H., Rich, J., Font-Ribera, A., et al. 2020, ApJ, 901, 153, doi: 10.3847/1538-4357/abb085 Duffy, L. D., & van Bibber, K. 2009, New J. Phys., 11, 105008, doi: 10.1088/1367-2630/11/10/105008 Dvorkin, C., et al. 2022, in Snowmass 2021. https://arxiv.org/abs/2203.07064 Grin, D., Amin, M. A., Gluscevic, V., et al. 2019. https://arxiv.org/abs/1904.09003 Hlozek, R., Grin, D., Marsh, D. J. E., & Ferreira, P. G. 2015, Phys. ˇ Rev. D, 91, 103512, doi: 10.1103/PhysRevD.91.103512 Hlozek, R., Marsh, D. J. E., & Grin, D. 2018, Mon. Not. Roy. ˇ Astron. Soc., 476, 3063, doi: 10.1093/mnras/sty271 Hlozek, R., Marsh, D. J. E., Grin, D., et al. 2017, Phys. Rev. D, 95, ˇ 123511, doi: 10.1103/PhysRevD.95.123511 Hu, W. 1998, Astrophys. J., 506, 485, doi: 10.1086/306274 Hu, W., Barkana, R., & Gruzinov, A. 2000, Phys. Rev. Lett., 85, 1158, doi: 10.1103/PhysRevLett.85.1158 Hwang, J.-c., & Noh, H. 2009, Phys. Lett. B, 680, 1, doi: 10.1016/j.physletb.2009.08.031 Irsiˇ c, V., Viel, M., Haehnelt, M. G., Bolton, J. S., & Becker, G. D. ˇ 2017a, Phys. Rev. Lett., 119, 031302, doi: 10.1103/PhysRevLett.119.031302 Irsiˇ c, V., et al. 2017b, Mon. Not. Roy. Astron. Soc., 466, 4332, ˇ doi: 10.1093/mnras/stw3372 Jaeckel, J., Mehta, V. M., & Witkowski, L. T. 2017, JCAP, 1701, 036, doi: 10.1088/1475-7516/2017/01/036 Kamionkowski, M., & Riess, A. G. 2022. https://arxiv.org/abs/2211.04492 Khlopov, M., Malomed, B. A., & Zeldovich, I. B. 1985, Mon. Not. Roy. Astron. Soc., 215, 575 Lague, A., Bond, J. R., Hlo ¨ zek, R., Marsh, D. J. E., & S ˇ oding, L. ¨ 2021, Mon. Not. Roy. Astron. Soc., 504, 2391, doi: 10.1093/mnras/stab601 Lee, A., Abitbol, M. H., Adachi, S., et al. 2019, in Bulletin of the American Astronomical Society, Vol. 51, 147, doi: 10.48550/arXiv.1907.08284 Leong, K.-H., Schive, H.-Y., Zhang, U.-H., & Chiueh, T. 2019, Mon. Not. Roy. Astron. Soc., 484, 4273, doi: 10.1093/mnras/stz271 Lewis, A., & Bridle, S. 2002, PhRvD, 66, 103511, doi: 10.1103/PhysRevD.66.103511 Lu, L., Sargent, W. L. W., Womble, D. S., & Takada-Hidai, M. 1996, Astrophys. J., 472, 509, doi: 10.1086/526756 Lyth, D. H. 1992, Phys. Rev. D, 45, 3394, doi: 10.1103/PhysRevD.45.3394 Mao, Y.-Y., et al. 2022. https://arxiv.org/abs/2203.07252 Marsh, D. J. E. 2016, Phys. Rept., 643, 1, doi: 10.1016/j.physrep.2016.06.005 Parashari, P., & Laha, R. 2023, Mon. Not. Roy. Astron. Soc., 526, L63, doi: 10.1093/mnrasl/slad107 Peccei, R. D., & Quinn, H. R. 1977, Phys. Rev. D, 16, 1791, doi: 10.1103/PhysRevD.16.1791 Poulin, V., Smith, T. L., & Karwal, T. 2023. https://arxiv.org/abs/2302.09032 Preskill, J., Wise, M. B., & Wilczek, F. 1983, Phys. Lett. B, 120, 127, doi: 10.1016/0370-2693(83)90637-8 Rogers, K. K., Hlozek, R., Lagu ˇ e, A., et al. 2023, JCAP, 06, 023, ¨ doi: 10.1088/1475-7516/2023/06/023 Rogers, K. K., & Peiris, H. V. 2021, Phys. Rev. Lett., 126, 071302, doi: 10.1103/PhysRevLett.126.071302 Runge, C. 1895, Mathematische Annalen, 46, 167. https://api.semanticscholar.org/CorpusID:119924854 Svrcek, P., & Witten, E. 2006, JHEP, 06, 051, doi: 10.1088/1126-6708/2006/06/051 Urena L ˜ opez, L. A. 2019. ´ https://arxiv.org/abs/1904.03318 Zhang, U.-H., & Chiueh, T. 2017a, Phys. Rev. D, 96, 063522, doi: 10.1103/PhysRevD.96.063522 —. 2017b, Phys. Rev., D96, 023507, doi: 10.1103/PhysRevD.96.023507

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