Understand
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.