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, $$f(Q,T)=\alpha Q+ \beta T$$f ( Q , T ) = α Q + β T , $$f(Q,T)=\alpha Q+ \beta T^2$$f ( Q , T ) = α Q + β T 2 , and $$f(Q,T)=Q+ \alpha Q^2+ \beta T$$f ( Q , T ) = Q + α Q 2 + β T . 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 $$f(Q,T)=\alpha Q+ \beta T$$f ( Q , T ) = α Q + β T with $$\beta =0$$β = 0 is completely equivalent to the GR case without cosmological constant $$\Lambda $$Λ . Further, we find that the model $$f(Q,T)=\alpha Q+ \beta T^2$$f ( Q , T ) = α Q + β T 2 with $$\beta \ne 0$$β ≠ 0 successfully depicts the observed transition from decelerated phase to an accelerated phase of the universe. Lastly, we find that the model $$f(Q,T)= Q+ \alpha Q^2+ \beta T$$f ( Q , T ) = Q + α Q 2 + β T with $$\alpha \ne 0$$α ≠ 0 represents an accelerated de-Sitter epoch for the constraints $$\beta < -1$$β < - 1 or $$ \beta \ge 0$$β ≥ 0 .