Maxwell-affine gauge theory of gravity

TL;DR

This paper develops a Maxwell-affine gauge theory of gravity by extending affine algebra with tensorial generators, deriving transformation rules, and proposing two invariant actions, with equations of motion satisfying generalized Bianchi identities.

Contribution

It introduces a novel Maxwell extension of affine algebra and constructs two invariant gravitational actions using nonlinear realization methods.

Findings

Derived transformation rules for Maxwell-affine algebra generators.

Presented two invariant gravitational actions, first and second order in affine curvature.

Showed equations of motion satisfy generalized Bianchi identities under specific conditions.

Abstract

Maxwell extension of affine algebra with additional tensorial generators is given. Using the methods of nonlinear realizations, we found the transformation rules for group parameters and corresponding generators. Gauging the Maxwell-affine algebra we presented two possible invariant actions for gravity: one is the first order and the other one is the second order in affine curvature. We noticed that equations of motion for the action, second order in affine curvature, lead to the generalized Bianchi identities on the choice of appropriate coefficients for a particular solution of the constraint equation.