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arXiv · 1704.06653

Noether Symmetry Analysis of Anisotropic Universe in Modified Gravity

M. Farasat Shamir·Fiza Kanwal
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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 $ΛCDM$ cosmology may be reconstructed for some suitable value of $n$.

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M. Farasat Shamir, Fiza Kanwal. 2017-04-21. Noether Symmetry Analysis of Anisotropic Universe in Modified Gravity. https://doi.org/10.1140/epjc%2Fs10052-017-4869-7

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