Gauging the Maxwell extended GL(n,R)\mathcal{GL}\left(n,\mathbb{R}\right) and SL(n+1,R)\mathcal{SL}\left(n+1,\mathbb{R}\right) algebras

We consider the extension of the general-linear and special-linear algebras by employing the Maxwell symmetry in $D$ space-time dimensions. We show how various Maxwell extensions of the ordinary spacetime algebras can be obtained by a suitable contraction of generalized algebras. The extended Lie algebras could be useful in the construction of generalized gravity theories and the objects that couple to them. We also consider the gravitational dynamics of these algebras in the framework of the gauge theories of gravity. By adopting the symmetry-breaking mechanism of the Stelle-West model, we present some modified gravity models that contain the generalized cosmological constant term.Comment: 14 page

Maxwell-modified metric affine gravity

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

Maxwell extension of

Inspired by the Maxwell symmetry generalization of general relativity (Maxwell gravity), we have constructed the Maxwell extension of f(R) gravity. We found that the semi-simple extension of the Poincare symmetry allows us to introduce geometrically a cosmological constant term in four-dimensional f(R) gravity. This symmetry also allows the introduction of a non-vanishing torsion to the Maxwell f(R) theory. It is found that the antisymmetric gauge field $$B^{ab}$$ associated with Maxwell extension is considered as a source of the torsion. It is also found that the gravitational equation of motion acquires a new term in the form of an energy–momentum tensor for the background field. The importance of these new equations is briefly discussed

Gauging the Maxwell Extended GLn,R and SLn+1,R Algebras

We consider the extension of the general-linear and special-linear algebras by employing the Maxwell symmetry in D space-time dimensions. We show how various Maxwell extensions of the ordinary space-time algebras can be obtained by a suitable contraction of generalized algebras. The extended Lie algebras could be useful in the construction of generalized gravity theories and the objects that couple to them. We also consider the gravitational dynamics of these algebras in the framework of the gauge theories of gravity. By adopting the symmetry-breaking mechanism of the Stelle–West model, we present some modified gravity models that contain the generalized cosmological constant term in four dimensions