Bounce universe from string-inspired Gauss-Bonnet gravity

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.PACS numbers: 04.50. Kd, 95.36.+x, 98.80.Cq

Inflationary Cosmology in Modified Gravity Theories

“…Especially, we present the consequences found in References [41,42]. The bouncing behaviors in various modified gravity theories have also been investigated in References [97][98][99][100][101][102]. We show that it is possible to reconstruct an F (R) gravity theory in which the matter bounce can happen in the framework of LQC.…”

Thermodynamics of nonsingular bouncing universes

“…(iii) Nonsingular bouncing universes. According to this proposal the universe experiences either just one contracting phase followed by an expanding one, or a sequence of expanding and contracting phases connected, in either case, to each other by a bounce such that the scale factor, a(t), of the Friedmann-RobertsonWalker (FRW) metric neither vanishes nor diverges [7][8][9][10][11][12] see [13] and [14] for reviews. Since the singularity theorems of Penrose and Hawking [15] forbid bounces to originate from normal matter the physics behind them is not straightforward and requires the presence of some source of energy that violates the null energy condition.…”

Towards the bounce inflationary gravitational wave

“…However, the physics of the bounce phase is unknown, it is obvious that the high-curvature corrections of gravity may also result in the occurrence of bounce, e.g., the GaussBonnet correction [49][50][51][52], and non-local gravity [53,54], which will inevitably modify the perturbation equation. We find that the corresponding corrections will aggravate the oscillating behavior around the cutoff scale H B+ , however, the spectrum in the regime of k H B− and k H B+ is hardly affected.…”