Physical aspects of ${ \boldsymbol{f}(\boldsymbol R,\boldsymbol G_{\boldsymbol\mu \boldsymbol\nu}\boldsymbol T^{\boldsymbol\mu \boldsymbol\nu})} $ modified gravity theories

Abstract：

The paper extends basic Einstein–Hilbert action by incorporating an invariant derived from a specific contraction between the Einstein tensor and energy momentum tensor. This represents a non–minimal coupling between the space–time geometry and matter fields. The fundamental Einstein–Hilbert action is extended by considering a generic function $ {f}(R,G_{\mu \nu}T^{\mu \nu}) $ . This function is subsequently dissected into its primary components: a geometric part reliant on the scalar curvature, and another segment encapsulating the interaction between geometry and matter fields. Distinct cosmological models are formulated at the backdrop of these dynamics, rooted in specific associations between the matter energy-momentum tensor and Einstein tensor. Upon deriving the consequent field equations, the cosmological model's physical implications are explored through a dynamical system analysis applied to diverse coupling functions. This exploration reveals that the current model aligns with various phases in the Universe's evolution, potentially elucidating several late-time historical epochs.