Semi-Symmetric Metric Gravity: A Brief Overview

Abstract: We present a review of the Semi-Symmetric Metric Gravity (SSMG) theory, representing a geometric extension of standard general relativity, based on a connection introduced by Friedmann and Schouten in 1924. The semi-symmetric connection is a connection that generalizes the Levi-Civita one, by allowing for the presence of a simple form of the torsion, described in terms of a torsion vector. The Einstein field equations are postulated to have the same form as in standard general relativity, thus relating the Einstein tensor constructed with the help of the semi-symmetric connection, with the energy-momentum tensor. The inclusion of the torsion contributions in the field equations has intriguing cosmological implications, particularly during the late-time evolution of the Universe. Presumably, these effects also dominate under high-energy conditions, and thus SSMG could potentially address unresolved issues in General Relativity and cosmology, such as the initial singularity, inflation, or the $^7$Li problem of the Big-Bang Nucleosynthesis. The explicit presence of torsion in the field equations leads to the non-conservation of the energy-momentum tensor, which can be interpreted within the irreversible thermodynamics of open systems, as describing particle creation processes. We also review in detail the cosmological applications of the theory, and investigate the statistical tests for several models, by constraining the model parameters via comparison with several observational datasets.