Torsion, Chern-Simons Term and Diffeomorphism Invariance

TL;DR

This paper explores the role of Chern-Simons modifications in gravity with torsion and their implications for diffeomorphism invariance, highlighting cancellations in the Bianchi identity and cosmological principles.

Contribution

It introduces a torsion-curvature framework for Chern-Simons gravity and analyzes its effects on fundamental symmetries and cosmological assumptions.

Findings

Chern-Simons contribution cancels in the Bianchi identity.

Homogeneity and isotropy relate to the strong equivalence principle.

Implications for diffeomorphism invariance in modified gravity.

Abstract

In the $torsion \otimes curvature$ approach of gravity Chern-Simons modification has been considered here. It has been found that Chern-Simons contribution to the bianchi identity has become cancelled from that of the scalar field part. But "homogeneity and isotropy" consideration of present day cosmology is a consequence of the "strong equivalence principle" and vice-versa.