Noether symmetry analysis of anisotropic universe in modified gravity

In this paper we study the anisotropic universe using Noether symmetries in modified gravity. In particular, we choose a locally rotationally symmetric Bianchi type-I universe for the analysis in f (R, G) gravity, where R is the Ricci scalar and G is the Gauss-Bonnet invariant. Firstly, a model f (R, G) = f(0)R(l) + f(1)G(n) is proposed and the corresponding Noether symmetries are investigated. We have also recovered the Noether symmetries for f (R) and f (G) theories of gravity. Secondly, some important cosmological solutions are reconstructed. Exponential and powerlaw solutions are reported for a well-known f (R, G) model, i.e., f (R, G) = f(0)R(n)G(1-n). Especially, 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.