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by Cosmological thinking: time, space and universal causation May 26th, 2024

This paper is available on arxiv under CC 4.0 license.

**Authors:**

(1) Rikpratik Sengupta, Department of Physics, Aliah University, Kolkata 700 160, West Bengal, India (E-mail addresses: [email protected](RS))

*Keywords*: oscillating universe, braneworld, bounce, turnaround, phantom.

The standard big bang model of cosmology is plagued by an initial singularity (at time t = 0), where the Friedmann equations describing the time evolution of the universe fails to render a plausible physical description of the space-time dynamics due to the diverging Hubble parameter H, which is a consequence of the infinitely large energy density prevailing in the very early universe. The scalar curvature R also diverges, implying that the initial singularity is a curvature singularity of the Ricci type, which are characterized by diverging energy densities. As shown in their famous singularity theorems by Hawking and Penrose, the initial big bang singularity cannot be avoided in a general relativistic (GR) setup provided the energy conditions are obeyed by matter filling up the universe[4, 5]. One of the key problems of the standard inflationary cosmology, besidies the ambiguity regarding the nature of the inflaton field is that, within the GR framework, inflation can not be past eternal[6]. So, if the inflation is preceeded by a radiation dominated phase, then the origin of the universe is singular. However, today many cosmologists are unhappy about the initial singularity and consider it to be a limitation of GR to describe space-times involving very large energy densities.

If there is no big bang, then the possibilities are that the universe either experiences a quantum creation where there is a quantum mechanical tunelling into an inflationary phase, or it may be that the universe existed for an eternally long time in a quasi static state followed by an emergent inflationary phase, or there is a non-singular bounce replacing the singular big bang prior to which the universe contracts and following which the universe expands. In the context of GR, the emergent and bouncing scenarios can be realised effectively only for a spatially closed universe (k = 1). A fully consistent treatment of the first possibility considering quantum creation will most probably require a quantum gravity (QG) treatment. However, there is no fully understood and developed QG theory at the moment and the two most accepted theories being worked on in this context are M-theory[7] involving extra dimensions and Loop Quantum Gravity (LQG)[8]. M- theory requires eleven space-time dimension for its quantum consistency while LQG quantizes space-time itself in the usual four dimensions. Effective theories from both the scenarios have become popular in recent times in the form of the extra dimensional braneworld models[9, 10] and the effective loop quantum cosmology (LQC)[11, 12] models.

It is interesting to note that although the premises of the background QG theories are completely different from each other, there are some similarities and identical features that may be obtained from a class of the effective braneworld and LQC models, that may hint at some hidden correspondance between the two contrasting approaches. In this letter, we shall only talk about models that introduce corrections to standard GR at the ultraviolet (UV) scale as we are concerned with resolution of the initial singularity. Braneworld models have the feature that our universe is represented by a (3 + 1)-dimensional hypersurface known as the ’brane’ (which are objects appearing in M-theory) embedded in a higher dimensional bulk spacetime. The Randall Sundrum single brane model (RS-II) is one such model with a spacelike extra dimension, indicating that the signature of the bulk space is Lorentzian. If the signature of the bulk deviates from the former, then we can have a bulk signature (−, −, +, +, +) such that the braneworld has a timelike extra dimension. The standard model particles and fields are confined to the brane, while gravity is free to propagate in the bulk.

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