Dark energy and Chern-Simons like gravity from a dynamical four-form

Abstract

We consider the dynamics of a four-form field $\tilde{w}$, treating it as a distinct physical degree of freedom, independent of the metric. The equations of motion are derived from an action which, besides having the standard Hilbert-Einstein term and the matter part, consists of a new action for $\tilde{w}$. The evolution of $\tilde{w}$ in a flat FRW universe is studied, and it is shown that the parameters of the theory admit solutions wherein it is possible to have an equation of state $p_{\varphi }\approx -{\epsilon }_{\varphi }$, so that it leads to an accelerating universe. We also put forward electromagnetic as well as gravitational `Chern-Simons' like terms that arise naturally in 4D, entailing a modified Einstein-Maxwell equation and an enlarged system of Einstein equation involving a Cotton tensor. We demonstrate that the scalar-density associated with $\tilde{w}$ can be employed to construct a generalized exterior derivative that converts a p-form density to a (p+1)-form density of identical weight.

arXiv commentElectromagnetic as well as gravitational Chern-Simons like terms associated with the four-form included, four references added

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