The Fate of the Universe Evolution in the Quadratic Form of Ricci-Gauss-Bonnet Cosmology

TL;DR

This paper explores the evolution and potential future singularities of the universe within quadratic Ricci-Gauss-Bonnet gravity models, showing stability and ruling out certain catastrophic fates.

Contribution

It introduces three quadratic $F(R,\, ext{G})$ gravity models and analyzes their physical properties and stability, advancing understanding of universe evolution without future singularities.

Findings

Models avoid future singularities and pseudo rip scenarios.

Stability of scalar perturbations is demonstrated.

Physical and geometrical properties of models are analyzed.

Abstract

We investigate the possibility of future singularity due to the accelerating expansion of the Universe. It has been found that the gravitational theory comprises Ricci scalar $R$ and Gauss-Bonnet invariant $\mathcal{G}$, known as $F(R,\mathcal{G})$ gravity, which can be viewed in the quadratic form. Three models are presented using Hubble parameters to represent a finite and infinite future. The parameters of the models are analyzed on the basis of their physical and geometrical properties. This study also explores the properties of the modified gravitational theory, and neither the future singularity nor the little or pseudo rip is posed as threats to the fate of the Universe. We present scalar perturbation approaches to perturbed evolution equations and demonstrate their stability.