f(Q, T) gravity, its covariant formulation, energy conservation and phase-space analysis

In the present article we analyze the matter-geometry coupled f(Q, T) theory of gravity. We offer the fully covariant formulation of the theory, with which we construct the correct energy balance equation and employ it to conduct a dynamical system analysis in a spatially flat Friedmann–Lemaître–Robertson–Walker spacetime. We consider three different functional forms of the f(Q, T) function, specifically, f(Q,T)=αQ+βT, f(Q,T)=αQ+βT2, and f(Q,T)=Q+αQ2+βT. We attempt to investigate the physical capabilities of these models to describe various cosmological epochs. We calculate Friedmann-like equations in each case and introduce some phase space variables to simplify the equations in more concise forms. We observe that the linear model f(Q,T)=αQ+βT with β=0 is completely equivalent to the GR case without cosmological constant Λ. Further, we find that the model f(Q,T)=αQ+βT2 with β≠0 successfully depicts the observed transition from decelerated phase to an accelerated phase of the universe. Lastly, we find that the model f(Q,T)=Q+αQ2+βT with α≠0 represents an accelerated de-Sitter epoch for the constraints β<-1 or β≥0.