Noether Symmetry Approach in $f(\mathcal{G},T)$ Gravity

Abstract

We explore the recently introduced modified Gauss-Bonnet gravity [1], $f(\mathcal{G},T)$ pragmatic with $\mathcal{G}$, the Gauss-Bonnet term, and $T$, the trace of the energy-momentum tensor. Noether symmetry approach has been used to develop some cosmologically viable $f(\mathcal{G},T)$ gravity models. The Noether equations of modified gravity are reported for flat FRW universe. Two specific models have been studied to determine the conserved quantities and exact solutions. In particular, the well known deSitter solution is reconstructed for some specific choice of $f(\mathcal{G},T)$ gravity model.

15 Pages, revised version, to appear in EPJC

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• Some Exact Solutions in $f(\mathcal{G},T)$ Gravity via Noether Symmetries
• Gravastars in $f(R,G)$ Gravity
• Noether Symmetry Approach in Energy-Momentum Squared Gravity
• Stellar Structures in $f(\mathcal{G})$ Gravity Admitting Noether Symmetries
• $f(\mathcal{R},\phi ,\chi )$ Cosmology with Noether Symmetry
• Energy Bounds in $f(R,G)$ Gravity with Anisotropic Background
• Noether Symmetries and Anisotropic Universe in Energy-Momentum Squared Gravity