f(R) Cosmology with torsion

Abstract

f (R)-gravity with geometric torsion (not related to any spin fluid) is considered in a cosmological context. We derive the field equations in vacuum and in presence of perfect-fluid matter and discuss the related cosmological models. Torsion vanishes in vacuum for almost all arbitrary functions f (R) leading to standard General Relativity. Only for f (R) = R 2 , torsion gives contribution in the vacuum leading to an accelerated behavior . When material sources are considered, we find that the torsion tensor is different from zero even with spinless material sources. This tensor is related to the logarithmic derivative of f ′ (R), which can be expressed also as a nonlinear function of the trace of the matter energy-momentum tensor Σµν . We show that the resulting equations for the metric can always be arranged to yield effective Einstein equations. When the homogeneous and isotropic cosmological models are considered, terms originated by torsion can lead to accelerated expansion. This means that, in f (R) gravity, torsion can be a geometric source for acceleration.

Updated f(T) gravity constraints from high-redshift cosmography

“…Moreover, a large part of the dark energy models so far proposed is based on the Einstein General Relativity (GR) theory of gravity, and it is therefore conceivable that the observed accelerating expansion could be interpreted as effects of alterations of the gravity action introduced in modified theories. Actually, in the last years different extensions to gravity have been widely investigated: by choosing the gravitational action as function of the Ricci scalar, f (R) 6 -, 7 or considering the framework of F (R, G) gravity in which F (R, G) is a generic function of the Ricci curvature scalar R and the Gauss-Bonnet topological invariant G, 8 or other curvature invariants. 9 In a quite different approach, avoiding the curvature defined via the Levi-Civita connection, it is possible to introduce and use an alternative connection that has no curvature (vanishing R ) but torsion T (teleparallelism gravity).…”

Stability in quadratic torsion theories

“…In the first place, the Cartan torsion is defined as the antisymmetric part of the affine connection as [4,[15][16][17] …”

Acceleration in Weyl Integrable Spacetime

“…[5]- [8] for comprehensive reviews and references). Less explored is the idea that the geometry of spacetime is not the so far assumed Lorentz geometry (see for example [9,10,11]). In this circumstance we need not only look for a new idea, but also revisit every type of the old models from a new viewpoint.…”