Scale Factor Duality for Conformal Cyclic Cosmologies

TL;DR

This paper explores how conformal time scale factor duality can be used to construct cyclic and pre-big-bang cosmological models, including extensions involving Gauss-Bonnet gravity, revealing new symmetries and thermodynamic properties.

Contribution

It demonstrates the application of conformal time SFD to develop pre-big-bang and cyclic models, including CCC and Gauss-Bonnet extensions, highlighting new symmetries and thermodynamic features.

Findings

Each big-bang model yields two different pre-big-bang evolutions.

Identified SFD symmetric cyclic universes with gauged Kähler sigma models.

Described thermodynamic features and second law conditions in Gauss-Bonnet extended models.

Abstract

The scale factor duality is a symmetry of dilaton gravity which is known to lead to pre-big-bang cosmologies. A conformal time version of the scale factor duality (SFD) was recently implemented as a UV/IR symmetry between decelerated and accelerated phases of the post-big-bang evolution within Einstein gravity coupled to a scalar field. The problem investigated in the present paper concerns the employment of the conformal time SFD methods to the construction of pre-big-bang and cyclic extensions of these models. We demonstrate that each big-bang model gives rise to two qualitatively different pre-big-bang evolutions: a contraction/expansion SFD model and Penrose's Conformal Cyclic Cosmology (CCC). A few examples of SFD symmetric cyclic universes involving certain gauged K\"ahler sigma models minimally coupled to Einstein gravity are studied. We also describe the specific SFD features of the thermodynamics and the conditions for validity of the generalized second law in the case of Gauss-Bonnet (GB) extension of these selected CCC models.