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 interpreted as geometrical inflaton vector fields which drive accelerated expansion.