Disformal vectors and anisotropies on a warped brane

TL;DR

This paper develops a dynamical system framework for analyzing anisotropic cosmologies with disformally coupled massive vector fields on a brane, revealing new fixed points and conditions for isotropy and acceleration.

Contribution

It introduces a systematic analysis of disformal vector fields in anisotropic cosmology, including new fixed points and a formalism applicable to various scenarios with extra dimensions.

Findings

Disformal coupling affects vector field dynamics and anisotropies.

Certain fixed points are not compatible with observed acceleration.

Models with rapid oscillations can preserve isotropy and mimic dark matter.

Abstract

The Maxwell action is conformally invariant and classically ignorant of conformally flat metrics. However, if the vector lives in a disformal metric--- as it does if residing upon a moving brane---this is no longer true. The disformal coupling is then mediated by a Dirac-Born-Infeld scalar field. Here a systematic dynamical system analysis is developed for anisotropic Bianchi I cosmology with a massive disformally coupled vector field. Several new fixed points are found, including anisotropic scaling solutions. The presented formalism here presented can be conveniently applied to general scenarios with or without extra dimensional motivations. This is illustrated here by performing a complete analysis with simple assumption that both the potentials and the warp factor for the brane are (nearly) exponential. In that case, the anisotropic fixed points are either not attractors, do not describe accelerating expansion or else they feature too large anisotropies to be compatible with observations. Nonetheless, viable classes of models exist where isotropy is retained due to rapid oscillations of the vector field, thus providing a possible realisation of disformally interacting massive dark matter.