Maxwell-modified metric affine gravity

Oktay Cebecioğlu,Salih Kibaroğlu

doi:10.1140/epjc/s10052-021-09685-6

Oktay Cebecioğlu, Salih Kibaroğlu

Open Access

https://doi.org/10.1140/epjc/s10052-021-09685-6

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Abstract

We present a gauge formulation of the special affine algebra extended to include an antisymmetric tensorial generator belonging to the tensor representation of the special linear group. We then obtain a Maxwell modified metric affine gravity action with a cosmological constant term. We find the field equations of the theory and show that the theory reduces to an Einstein-like equation for metric affine gravity with the source added to the gravity equations with cosmological constant mu contains linear contributions from the new gauge fields. The reduction of the Maxwell metric affine gravity to Riemann–Cartan one is discussed and the shear curvature tensor corresponding to the symmetric part of the special linear connection is identified with the dark energy. Furthermore, the new gauge fields are interpreted as geometrical inflaton vector fields which drive accelerated expansion.

Highlights

It is verified by the Solar System and cosmological tests that general relativity provides an elegant and powerful formulation of gravitation in terms of Riemannian geometry and forms our understanding of space-time [1]
There are some reasons to believe that general relativity is unable to explain some gravity phenomena on both atomic and cosmological scales and should be either modified or replaced by a new theory of gravity
By gauging Maxwell symmetries, one can define modified gravitational theories that extend general relativity by including a generalized cosmological term [20,21,22,23,24,25,26,27,28,29,30]. Among these is the Maxwell extension of special affine symmetry and its gauging which will be the focus of our attention in this paper

Summary

Introduction

It is verified by the Solar System and cosmological tests that general relativity provides an elegant and powerful formulation of gravitation in terms of Riemannian geometry and forms our understanding of space-time [1]. By gauging Maxwell symmetries, one can define modified gravitational theories that extend general relativity by including a generalized cosmological term [20,21,22,23,24,25,26,27,28,29,30]. Among these is the Maxwell extension of special affine symmetry and its gauging which will be the focus of our attention in this paper.

Introducing the special-affine algebra and its maxwell extension

Gauging the Maxwell-specıal-affine algebra

Rφab 2

Constructıon of the metric for the affine space

Maxwell-modified mag field equations

Conclusion