Bouncing cosmology in modified Gauss–Bonnet gravity

Abstract

We explore bounce cosmology in F (G) gravity with the Gauss-Bonnet invariant G. We reconstruct F (G) gravity theory to realize the bouncing behavior in the early universe and examine the stability conditions for its cosmological solutions. It is demonstrated that the bouncing behavior with an exponential as well as a power-law scale factor naturally occurs in modified Gauss-Bonnet gravity. We also derive the F (G) gravity model to produce the ekpyrotic scenario. Furthermore, we construct the bounce with the scale factor composed of a sum of two exponential functions and show that not only the early-time bounce but also the late-time cosmic acceleration can occur in the corresponding modified Gauss-Bonnet gravity. Also, the bounce and late-time solutions in this unified model is explicitly analyzed.Introduction-As a cosmological model to describe the early universe, the matter bounce scenario [1] is known. In this scenario, in the contraction phase the universe is dominated by matter, and a non-singular bounce occurs. Also, the density perturbations whose spectrum is consistent with the observations can be produced (for a review, see [2]). In addition, after the contracting phase, the so-called BKL instability [3] happens, so that the universe will be anisotropic. The way of avoiding this instability [4] and issues of the bounce [5] in the Ekpyrotic scenario [6] has been investigated [7,8]. Moreover, the density perturbations in the matter bounce scenario with two scalar fields has recently been examined [9].On the other hand, various cosmological observations support the current cosmic accelerated expansion. To explain this phenomenon in the homogeneous and isotropic universe, it is necessary to assume the existence of dark energy, which has negative pressure, or propose that gravity is modified on large scales (for recent reviews on issues of dark energy and modified gravity theories, see, e.g., [10,11]). Regarding the latter approach, there have been proposed a number of modified gravity theories such as F (R) gravity. The bouncing behavior has been investigated in F (R) gravity [12][13][14][15], string-inspired gravitational theories [16], non-local gravity [17]. A relation between the bouncing behavior and the anomalies on the cosmic microwave background (CMB) radiationhas also been discussed [18].In this Letter, we explore bounce cosmology in F (G) gravity with F (G) an arbitrary function of the Gauss-Bonnet invariant G = R 2 −4R µν R µν +R µνρσ R µνρσ , where R µν is the Ricci tensor and R µνρσ is the Riemann tensor. Such F (G) theory has been proposed as gravitational alternative for dark energy and inflation in Ref. [19] and its application to the late-time cosmology [20] has been studied. Moreover, cosmology in a theory with a dynamical dilaton coupling to the Gauss-Bonnet invariant has also been studied [21]. We use units of k B = c l = = 1, where c is the speed of light, and denote the gravitational constant 8πG by κ 2 ≡ 8π/M Pl 2 with the Planck mass of M Pl = G −1/2 = 1.2 × 10 19 GeV. In the followin...

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.…”

A critical review of classical bouncing cosmologies

“…The same technique of Lagrangian reconstruction can be used assuming a function of the Gauss-Bonnet invariant G ≡ R 2 − 4R µν R µν + R µναβ R µναβ instead of one of the curvature Ricci scalar R. Bouncing solutions were explored in [296], some of which were found to be stable.…”

Gauss-Bonnet cosmology unifying late and early-time acceleration eras with intermediate eras

“…To this end we shall use well known reconstruction techniques [2,14,[16][17][18], and we investigate which F (G) gravity can approximately generate each era of the model (1). Consider the following Jordan frame vacuum F (G) gravity action,…”

“…[8] was realized in the context of an F (R) gravity, in this paper we will realize the cosmological evolution of Ref. [8], but in the context of F (G) gravity [9,[11][12][13][14][15][16][17][18][19], see also Refs. [2][3][4][5][6] for reviews.…”