Cosmological perturbations in extended electromagnetism: General gauge invariant approach

Abstract

A certain vector-tensor theory is revisited. It was proposed and analyzed as a theory of electromagnetism without the standard gauge invariance. Our attention is first focused on a detailed variational formulation of the theory, which leads to both a modified Lorentz force and the true energy-momentum tensor of the vector field. The theory is then applied to cosmology. A complete gauge invariant treatment of the scalar perturbations is presented. For appropriate gauge invariant variables describing the scalar modes of the vector field (A modes), it is proved that the evolution equations of these modes do not involve the scalar modes appearing in general relativity (GR modes), which are associated to the metric and the energy-momentum tensor of the cosmological fluids. However, the A modes modify the standard gauge invariant equations describing the GR modes. By using the new formalism, the evolution equations of the A perturbations are derived and separately solved and, then, the correction terms—due to the A perturbations—appearing in the evolution equations of the GR modes are estimated. The evolution of these correction terms is studied for an appropriate scale. The relevance of these terms depends on both the spectra and the values of the normalization constants involved in extended electromagnetism. Further applications of the new formalism will be presented elsewhere.