Four-form field versus fundamental scalar field

Abstract

A modified-gravity theory with a four-form field strength F, a variable gravitational coupling parameter G(F), and a standard matter action are considered here. Maxwell and Einstein equations are now derived when including to action also derivates of F. The energy momentum tensor of the 4-form field contains both the part, which is typical for the fundamental (pseudo)scalar, and the part, which cancels the divergent contribution of the zero-point energies of quantum fields to the vacuum energy and thus leads to the natural nullification of the cosmological constant in Minkowski vacuum.