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

Abstract In the present article we analyze matter-geometry coupled f ( Q , T ) theory of gravity. We offer fully covariant formulation theory, with which construct correct energy balance equation and employ it to conduct a dynamical system analysis in spatially flat Friedmann–Lemaître–Robertson–Walker spacetime. consider three different functional forms function, specifically, $$f(Q,T)=\alpha Q+ \beta T$$ f ( Q , T ) = α + β T^2$$ 2 $$f(Q,T)=Q+ \alpha Q^2+ . attempt investigate physical capabilities these models describe various cosmological epochs. calculate Friedmann-like equations each case introduce some phase space variables simplify more concise forms. observe that linear model $$\beta =0$$ 0 is completely equivalent GR without constant $$\Lambda $$ Λ Further, find \ne 0$$ ≠ successfully depicts observed transition from decelerated an accelerated universe. Lastly, $$f(Q,T)= $$\alpha represents de-Sitter epoch for constraints < -1$$ < - 1 or \ge ≥