f(R) cosmology with torsion

TL;DR

This paper explores how torsion in f(R) gravity can induce accelerated expansion in cosmological models, acting as a geometric source for acceleration even without spin fluids.

Contribution

It demonstrates that torsion in f(R) gravity can cause acceleration in cosmology, especially highlighting the special case f(R)=R^2 where torsion contributes in vacuum.

Findings

Torsion vanishes in vacuum for most f(R), recovering GR.

For f(R)=R^2, torsion contributes to vacuum acceleration.

Torsion remains non-zero with matter, influencing cosmic acceleration.

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. 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.