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

TL;DR

This paper explores a four-form field as a new degree of freedom in gravity, showing it can drive cosmic acceleration and introduces Chern-Simons-like terms affecting Einstein's equations.

Contribution

It introduces a dynamical four-form field in gravity, deriving its equations of motion, and demonstrates its potential to produce an accelerating universe with novel Chern-Simons-like modifications.

Findings

Four-form field can lead to accelerated expansion in a flat FRW universe.

Chern-Simons-like terms naturally arise, modifying Einstein-Maxwell equations.

Scalar-density from the four-form enables a generalized exterior derivative.

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_\phi \approx -\epsilon_\phi $, 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.