This paper is devoted to investigate the recently proposed modified Gauss-Bonnet $f(\mathcal{ G},T)$ gravity, with $\mathcal{ G}$, the Gauss-Bonnet term, coupled with ${ T}$, the trace of energy-momentum tensor. We have used the Noether symmetry methodology to discuss some cosmologically important $f(\mathcal{ G},T)$ gravity models with anisotropic background. In particular, the Noether symmetry equations for modified $f(\mathcal{ G},T)$ 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 Gauss-Bonnet gravity may be used to reconstruct $\Lambda$CDM cosmology without involving any cosmological constant.
Categories: gr-qc