Bouncing Cosmology in Modified Gravity with Higher-Order Gauss–Bonnet Curvature Term

Abstract

In this paper, we studied the bouncing behavior of the cosmological models formulated in the background of the Hubble function in the F(R,G) theory of gravity, where R and G, respectively, denote the Ricci scalar and Gauss–Bonnet invariant. The actions of the bouncing cosmology are studied with a consideration of the different viable models that can resolve the difficulty of singularity in standard Big Bang cosmology. Both models show bouncing behavior and satisfy the bouncing cosmological properties. Models based on dynamical, deceleration, and energy conditions indicate the accelerating behavior at the late evolution time. The phantom at the bounce epoch is analogous to quintessence behavior. Finally, we formulate the perturbed evolution equations and investigate the stability of the two bouncing solutions.

Probing bounce dynamics via Higher-Order Gauss-Bonnet modifications

“…In the following, we detail the technique for reconstructing models of Higher-Order Gauss-Bonnet Gravity. This approach, as outlined in references [39][40][41], involves the incorporation of suitable functions, namely P and Q, which are functions of a scalar field t representing cosmic time. By employing these functions, the action described in equation (1) in the absence of matter can be expressed as follows:…”

Bouncing Cosmology in f(R,G)$f(R,\mathcal {G})$ Gravity with Thermodynamic Analysis

“…When a(t) approaches a non-zero minimum value in the close domain of the bouncing point, the model is called a non-singular bouncing model. The concept of the bouncing behavior of the universe has been explored by numerous researchers across various alternative gravity theories, such as f (R), [51][52][53][54][55] f (R, T), [56][57][58][59][60] f (𝒢), [61][62][63] f (R, 𝒢), [64][65][66] f (𝒢, T), [67,68] f (Q), [69,70] etc. Cai et al have conducted notable research on a non-singular bouncing cosmological model.…”

“…The concept of the bouncing behavior of the universe has been explored by numerous researchers across various alternative gravity theories, such as $$ f(R)$$, [ 51–55 ] $$ f(R,T)$$, [ 56–60 ] $$ f(\mathcal {G})$$, [ 61–63 ] $$ f(R,\mathcal {G})$$, [ 64–66 ] $$ f(\mathcal {G},T)$$, [ 67,68 ] $$ f(Q)$$, [ 69,70 ] etc. Cai et al.…”

Energy Conditions with Interacting Field in f(R) Gravity

“…Some authors [32] presented a FRW cosmological model which satisfied the principle and considering the most recent research that suggested dark energy is responsible for the Universe's acceleration. The authors [33] selected a specific functional form and explored the cosmological behavior of FRW models in the f (R, G) gravity. They discussed violations of the SEC (strong energy condition) and NEC (null energy condition), which are necessary for bouncing models.…”