Some Exact Solutions in $f(\mathcal{G},T)$ Gravity via Noether Symmetries

TL;DR

This paper investigates exact solutions in $f( ext{G},T)$ gravity using Noether symmetries, proposing models that can replicate $ ext{Lambda}$CDM cosmology without a cosmological constant.

Contribution

It introduces specific $f( ext{G},T)$ gravity models with anisotropic backgrounds and derives exact solutions via Noether symmetry analysis.

Findings

Models can reproduce $ ext{Lambda}$CDM cosmology without a cosmological constant.

Explicit solutions and conserved quantities are obtained for Bianchi type I universe.

Modified gravity models show potential for explaining cosmic acceleration.

Abstract

This paper is devoted to investigate the recently proposed modified Gauss-Bonnet $f(\mathcal{G},T)$ gravity, with $\mathcal{G}$, the Gauss-Bonnet term, coupled with ${T}$, the trace of energy-momentum tensor. We have used the Noether symmetry methodology to discuss some cosmologically important $f(\mathcal{G},T)$ gravity models with anisotropic background. In particular, the Noether symmetry equations for modified $f(\mathcal{G},T)$ gravity are reported for locally rotationally symmetric Bianchi type $I$ universe. Explicitly, two models have been proposed to explore the exact solutions and the conserved quantities. It is concluded that the specific models of modified Gauss-Bonnet gravity may be used to reconstruct $\Lambda$CDM cosmology without involving any cosmological constant.