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

• Main Authors: Loo, Tee-How, Solanki, Raja, De, Avik, Sahoo, P. K.
• Format: Article
• Published: Springer 2023
• Subjects: QA Mathematics
• Online Access: http://eprints.um.edu.my/38401/

In the present article we analyze the mattergeometry 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-Lemaitre-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 not equal 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 a not equal 0 represents an accelerated de-Sitter epoch for the constraints beta < -1 or beta = 0.