https://doi.org/10.1140/epjc/s10052-020-8023-6
Regular Article - Theoretical Physics
Weyl type f(Q, T) gravity, and its cosmological implications
1
School of Physics, Sun Yat-Sen University, Guangzhou, 510275, People’s Republic of China
2
Astronomical Observatory, 19 Ciresilor Street, 400487, Cluj-Napoca, Romania
3
Department of Physics, Babes-Bolyai University, Kogalniceanu Street, 400084, Cluj-Napoca, Romania
4
School of Physics, Damghan University, Damghan, 41167-36716, Iran
5
State Key Laboratory of Optoelectronic Material and Technology, Guangdong Province Key Laboratory of Display Material and Technology, Sun Yat-Sen University, Guangzhou, People’s Republic of China
* e-mail: tiberiu.harko@aira.astro.ro
Received:
19
March
2020
Accepted:
6
May
2020
Published online:
20
May
2020
We consider an f(Q, T) type gravity model in which the scalar non-metricity 
of the space-time is expressed in its standard Weyl form, and it is fully determined by a vector field 
. The field equations of the theory are obtained under the assumption of the vanishing of the total scalar curvature, a condition which is added into the gravitational action via a Lagrange multiplier. The gravitational field equations are obtained from a variational principle, and they explicitly depend on the scalar nonmetricity and on the Lagrange multiplier. The covariant divergence of the matter energy-momentum tensor is also determined, and it follows that the nonmetricity-matter coupling leads to the nonconservation of the energy and momentum. The energy and momentum balance equations are explicitly calculated, and the expressions of the energy source term and of the extra force are found. We investigate the cosmological implications of the theory, and we obtain the cosmological evolution equations for a flat, homogeneous and isotropic geometry, which generalize the Friedmann equations of standard general relativity. We consider several cosmological models by imposing some simple functional forms of the function f(Q, T), and we compare the predictions of the theory with the standard 
CDM model.
© The Author(s), 2020
