# Noether Symmetry Analysis of Anisotropic Universe in Modified Gravity

## TL;DR

This paper explores anisotropic universe models in modified gravity using Noether symmetries, deriving solutions like exponential, power law, and Kasner's, and connecting them to cosmological scenarios such as de-Sitter and $ ext{Λ}$CDM.

## Contribution

It identifies Noether symmetries in $f(R, ext{G})$ gravity for anisotropic universes and reconstructs relevant cosmological solutions, including de-Sitter and Kasner's solutions.

## Key findings

- Recovered Noether symmetries for $f(R)$ and $f( ext{G})$ theories.
- Derived exponential and power law solutions in $f(R, ext{G})$ models.
- Reconstructed Kasner's and de-Sitter solutions relevant to cosmology.

## Abstract

In this paper, we study anisotropic universe using Noether symmetries in modified gravity. In particular, we choose locally rotationally symmetric Bianchi type-$I$ universe for the analysis in $f(R,\mathcal{G})$ gravity, where $R$ is the Ricci scalar and $\mathcal{G}$ is the Gauss-Bonnet invariant. Firstly, a model $f(R,\mathcal{G})=f_0R^l+f_1\mathcal{G}^n$ is proposed and the corresponding Noether symmetries are investigated. Further, we have also recovered the Noether symmetries for $f(R)$ and $f(\mathcal{G})$ theories of gravity. Secondly, some important cosmological solutions are reconstructed. Exponential and power law solutions are reported for a well-known $f(R,\mathcal{G})$ model, i.e., $f(R,\mathcal{G})=f_0R^n\mathcal{G}^{1-n}$. Especially, the Kasner's solution is recovered and it is anticipated that the familiar de-Sitter spacetime giving $\Lambda CDM$ cosmology may be reconstructed for some suitable value of $n$.