Bounce universe from string-inspired Gauss-Bonnet gravity

TL;DR

This paper investigates bouncing cosmologies within string-inspired Gauss-Bonnet gravity, reconstructing scalar field potentials and couplings, and analyzing frame transformations to understand the properties of the bounce in different conformal frames.

Contribution

It reconstructs scalar potentials and Gauss-Bonnet couplings for bounce solutions and examines their behavior under conformal transformations between string and Einstein frames.

Findings

Bounce solutions are realized with hyperbolic and exponential scale factors.

The bounce property changes between string and Einstein frames.

Gauss-Bonnet coupling appears at the bounce in the Einstein frame, but not in the string frame.

Abstract

We explore cosmology with a bounce in Gauss-Bonnet gravity where the Gauss-Bonnet invariant couples to a dynamical scalar field. In particular, the potential and and Gauss-Bonnet coupling function of the scalar field are reconstructed so that the cosmological bounce can be realized in the case that the scale factor has hyperbolic and exponential forms. Furthermore, we examine the relation between the bounce in the string (Jordan) and Einstein frames by using the conformal transformation between these conformal frames. It is shown that in general, the property of the bounce point in the string frame changes after the frame is moved to the Einstein frame. Moreover, it is found that at the point in the Einstein frame corresponding to the point of the cosmological bounce in the string frame, the second derivative of the scale factor has an extreme value. In addition, it is demonstrated that at the time of the cosmological bounce in the Einstein frame, there is the Gauss-Bonnet coupling function of the scalar field, although it does not exist in the string frame.