f(Q, T) gravity, its covariant formulation, energy conservation and phase-space analysis
Tee-How Loo (Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur, 50603, Malaysia); Raja Solanki (Department of Mathematics, Birla Institute of Technology and Science-Pilani, Hyderabad Campus, Hyderabad, 500078, India); Avik De (Department of Mathematical and Actuarial Sciences, Universiti Tunku Abdul Rahman, Jalan Sungai Long, Cheras, 43000, Malaysia); P. Sahoo (Department of Mathematics, Birla Institute of Technology and Science-Pilani, Hyderabad Campus, Hyderabad, 500078, India)
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, $$f(Q,T)=\alpha Q+ \beta T$$ , $$f(Q,T)=\alpha Q+ \beta T^2$$ , and $$f(Q,T)=Q+ \alpha Q^2+ \beta T$$ . 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 $$f(Q,T)=\alpha Q+ \beta T$$ with $$\beta =0$$ is completely equivalent to the GR case without cosmological constant $$\Lambda $$ . Further, we find that the model $$f(Q,T)=\alpha Q+ \beta T^2$$ with $$\beta \ne 0$$ successfully depicts the observed transition from decelerated phase to an accelerated phase of the universe. Lastly, we find that the model $$f(Q,T)= Q+ \alpha Q^2+ \beta T$$ with $$\alpha \ne 0$$ represents an accelerated de-Sitter epoch for the constraints $$\beta < -1$$ or $$ \beta \ge 0$$ .