Generalized cosmological term from Maxwell symmetries

Abstract

By gauging the Maxwell spacetime algebra the standard geometric framework of Einstein gravity with cosmological constant term is extended by adding six fourvector fields A_\mu^{ab}(x) associated with the six abelian tensorial charges in the Maxwell algebra. In the simplest Maxwell extension of Einstein gravity this leads to a generalized cosmological term that includes a contribution from these vector fields. We also consider going beyond the basic gravitational model by means of bilinear actions for the new Abelian gauge fields. Finally, an analogy with the supersymmetric generalization of gravity is indicated. In an Appendix, we propose an equivalent description of the model in terms of a shift of the standard spin connection by the A_\mu^{ab}(x) fields.Comment: 7 pages, RevTex style. Enlarged version to appear in PR

Gauge theory of the Maxwell-Weyl group

“…Soroka [25] presented another approach to the problem but this time gauging semi-simple extension of Poincare algebra. The formulation of different types of Maxwell gravities has already been done in [26][27][28]. With this motivation, we have presented the gauge theory of Maxwell-Weyl group denoted by MW (1, 3).…”

“…J.A. de Azcarraga in his paper [26] achived the generalized cosmological constant problem by gauging the Maxwell algebra, later D.V. Soroka [25] presented another approach to the problem but this time gauging semi-simple extension of Poincare algebra.…”

Maxwell Symmetries and Some Applications

“…In this paper, following [6], we present the construction of a local D = 4 gauge theory based on the Maxwell algebra (eqs. (1,2)) and apply it to generalize Einstein gravity.…”

“…The second term in the rhs of (23) provides a field-dependent modification of the cosmological constant at the lhs of the equation. We wish to add that: 1) Using equations (15) and (16), the spin connection may be expressed as a function ω ab (e, A) of the vierbein and the new gauge fields (for perturbative solutions see [6], Appendix). In such a way we obtain the second order formulation of Maxwell gravity, with independent fields e a µ and A ab µ .…”

Gauge semi-simple extension of the Poincaré group

“…was given by de Azcarraga, Kamimura and Lukierski [20]. Here Z ab is a tensor generator, g ab is a constant Minkovski metric and c is some constant.…”