Energy Conditions in $f(\mathcal{G},T)$ Gravity

TL;DR

This paper introduces a new modified gravity theory called $f( ext{G},T)$ gravity, formulates its field equations, and investigates energy conditions within FRW cosmology, applying reconstruction techniques to specific solutions.

Contribution

It proposes a novel $f( ext{G},T)$ gravity model, derives its energy conditions, and applies reconstruction methods to analyze cosmological solutions.

Findings

Energy conditions are expressed in terms of cosmological parameters.

Feasible constraints on model parameters are obtained from energy bounds.

Reconstruction of de Sitter and power-law solutions demonstrates the model's viability.

Abstract

The aim of this paper is to introduce a new modified gravity theory named as $f(\mathcal{G},T)$ gravity ($\mathcal{G}$ and $T$ are the Gauss-Bonnet invariant and trace of the energy-momentum tensor, respectively) and investigate energy conditions for two reconstructed models in the context of FRW universe. We formulate general field equations, divergence of energy-momentum tensor, equation of motion for test particles as well as corresponding energy conditions. The massive test particles follow non-geodesic lines of geometry due to the presence of extra force. We express energy conditions in terms of cosmological parameters like deceleration, jerk and snap parameters. The reconstruction technique is applied to this theory using de Sitter and power-law cosmological solutions. We analyze energy bounds and obtain feasible constraints on free parameters.