Weyl type f(Q, T) gravity, and its cosmological implications

Abstract

We consider an f(Q, T) type gravity model in which the scalar non-metricity $$Q_{\alpha \mu \nu }$$Qαμν of the space-time is expressed in its standard Weyl form, and it is fully determined by a vector field $$w_{\mu }$$wμ. 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 $$\Lambda $$ΛCDM model.

Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type f(Q, T) gravity

“…In particular, the role of matter and of the geometry-matter couplings have been analyzed in [99,104], respectively. In the present paper we have extended the previous analyses of the Weyl-type f (Q, T ) gravity, a particular version of the general f (Q, T ) type theories, by developing some basic theoretical tools that would allow one not only to make further investigations of the fundamental geometrical and physical properties of these gravity theories, but they can also open the possibility of their observational testing.…”

“…A particular model of the general f (Q, T ) theory was introduced in [104], and it is based on the following action:…”

“…A particular type of f (Q, T ) model was considered in [104], in which the scalar non-metricity Q μν of the spacetime was expressed in its standard Weyl form, and therefore it is fully determined by a vector field w μ . The field equations of the theory have been obtained under the assumption of the vanishing of the total scalar curvature, a condition which was added into the gravitational action via a Lagrange multiplier.…”

“…The main goal of the present paper is to investigate some fundamental properties of the motion of test particles in the Weyl type f (Q, T ) gravity theory, introduced in [104]. We derive the geodesic deviation equation and the Raychaudhuri equation in the Weyl geometry and in the presence of the extra force that describes the effects of the non-metricitymatter coupling.…”

f(Q,T) gravity models with observational constraints

“…In [8], the authors studied inflationary and late time cosmology in f (T , T ) gravity where T and T are torsion and trace of energy momentum tensor. A very recent study of Yixin [9] shows the non-minimal coupling between Q and T taking into account some different class of cosmological models with some specific functional forms of f (Q, T ). Different forms of f (Q, T ) can result in obtaining a large variety of cosmological evolution including the deceleration and acceleration expansions.…”