Energy Bounds in $f(R,G)$ Gravity with Anisotropic Background

TL;DR

This paper examines energy bounds in anisotropic $f(R,G)$ gravity models, analyzing their viability through energy conditions and cosmological parameters, with some models satisfying all conditions and others indicating cosmic expansion.

Contribution

It introduces a detailed analysis of energy bounds in anisotropic $f(R,G)$ gravity models, including viability assessment via energy conditions and cosmological parameters.

Findings

First two models satisfy NEC, WEC, and SEC under certain conditions.

Third and fourth models violate SEC, indicating cosmic expansion.

Graphical analysis supports the viability of specific models.

Abstract

This paper investigates the energy bounds in modified Gauss-Bonnet gravity with anisotropic background. Locally rotationally symmetric Bianchi type ${I}$ cosmological model in $f(R,G)$ gravity is considered to meet this aim. Primarily, a general $f(R,G)$ model is used to develop the field equations. In this aspect, we investigate the viability of modified gravitational theory by studying the energy conditions. We take in account four $f(R,G)$ gravity models commonly discussed in the literature. We formulate the inequalities obtained by energy conditions and investigate the viability of the above mentioned models using the Hubble, deceleration, jerk and snap parameters. Graphical analysis shows that for first two $f(R,G)$ gravity models, NEC, WEC and SEC are satisfied under suitable values of anisotropy and model parameters involved. Moreover, SEC is violated for the third and fourth models which predicts the cosmic expansion.