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Noether Symmetry Analysis of Anisotropic Universe in Modified Gravity (1704.06653v1)

Published 21 Apr 2017 in gr-qc

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 $f(R,\mathcal{G})=f_0Rl+f_1\mathcal{G}n$ 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., $f(R,\mathcal{G})=f_0Rn\mathcal{G}{1-n}$. 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 $n$.

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