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

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

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