Is torsion needed in theory of gravity?

TL;DR

This paper reviews the role of torsion in gravity theories, arguing that current experimental evidence and theoretical considerations support the sufficiency of General Relativity's Lorentzian manifold without torsion.

Contribution

It provides a comprehensive review of torsion in gravity theories, emphasizing the lack of experimental evidence and presenting theoretical arguments against torsion's necessity.

Findings

No experimental evidence for torsion in nature.

Tests of Einstein Equivalence Principle support GR.

Theoretical arguments favor torsion-free models.

Abstract

It is known that General Relativity ({\bf GR}) uses Lorentzian Manifold $(M_4;g)$ as a geometrical model of the physical space-time. $M_4$ means here a four-dimensional differentiable manifold endowed with Lorentzian metric $g$. The metric $g$ satisfies Einstein equations. Since the 1970s many authors have tried to generalize this geometrical model of the physical space-time by introducing torsion and even more general metric-affine geometry. In this paper we discuss status of torsion in the theory of gravity. At first, we emphasize that up to now we have no experimental evidence for the existence of torsion in Nature. Contrary, the all experiments performed in weak gravitational field (Solar System) or in strong regime (binary pulsars) and tests of the Einstein Equivalence Principle ({\bf EEP}) confirmed {\bf GR} and Lorentzian manifold $(M_4;g)$ as correct geometrical model of the physical space-time. Then, we give theoretical arguments against introducing of torsion into geometrical model of the physical space-time. At last, we conclude that the general-relativistic model of the physical space-time is sufficient and it seems to be the most satisfactory.