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

Tee-How Loo; Raja Solanki; Avik De; P. K. Sahoo

doi:10.1140/epjc/s10052-023-11391-4

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 261
https://doi.org/10.1140/epjc/s10052-023-11391-4

Regular Article - Theoretical Physics

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

Tee-How Loo¹, Raja Solanki², Avik De³^c and P. K. Sahoo²

¹ Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, 50603, Kuala Lumpur, Malaysia
² Department of Mathematics, Birla Institute of Technology and Science-Pilani, Hyderabad Campus, 500078, Hyderabad, India
³ Department of Mathematical and Actuarial Sciences, Universiti Tunku Abdul Rahman, Jalan Sungai Long, 43000, Cheras, Malaysia

^c avikde@utar.edu.my

Received: 2 March 2023
Accepted: 5 March 2023
Published online: 28 March 2023

Abstract

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

© The Author(s) 2023

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