In this paper, we have studied the bouncing behaviour of the cosmological models formulated at the background of Hubble function in F(R, G) theory of gravity, where R and G respectively denotes the Ricci scalar and Gauss-Bonnet invariant. The actions of bouncing cosmology are studied under consideration of different viable models and can resolve the difficulty of singularity in standard Big-Bang cosmology. Both the models are showing bouncing behaviour and satisfying the bouncing cosmological properties. Models based on dynamical, deceleration, and energy conditions indicate the accelerating behavior at the late evolution time. Phantom at the bounce epoch is analogous to a quintessence behavior. Finally, we formulate the perturbed evolution equations and investigate the stability of two bouncing solutions.
The ultimate fate of the Universe or the possible occurrence of future singularity to interpret the cosmic accelerating expansion phenomena has been discussed in this paper. The gravitational theory comprising of Ricci scalar R and Gauss-Bonnet invariant G, known as f (R, G) gravity has been considered in the quadratic form. Three models with the Hubble parameter that represents finite and infinite future time are presented. The physical and geometrical parameters of the models are analysed. Also, the properties of modified gravitational theory have been examined. The fate of the Universe evolution in this study confronts with neither little or pseudo rip nor the future singularity. The perturbed evolution equations are formulated in the scalar perturbation approach and the stability of the models are shown.
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