Abstract
This paper is devoted to investigate the recently proposed modified GaussāBonnet [Formula: see text] gravity, with [Formula: see text], the GaussāBonnet term, coupled with [Formula: see text], the trace of energyāmomentum tensor. We have used the Noether symmetry methodology to discuss some cosmologically important [Formula: see text] gravity models with anisotropic background. In particular, the Noether symmetry equations for modified [Formula: see text] 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 GaussāBonnet gravity may be used to reconstruct [Formula: see text]CDM cosmology without involving any cosmological constant.
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