The Self-Accelerating Universe with Vectors in Massive Gravity

TL;DR

This paper investigates self-accelerating cosmological solutions in massive gravity including vector modes, revealing ghost instabilities with background vectors but stable solutions without them, unaffected by a bare cosmological constant.

Contribution

It demonstrates the existence of self-accelerating solutions with vector fields in massive gravity and analyzes their stability, highlighting ghost issues linked to background vectors.

Findings

Ghost instabilities occur with background vector fields.

Ghosts are avoided when background vectors are absent, but at strong coupling.

A bare cosmological constant does not induce ghosts or alter stability conclusions.

Abstract

We explore the possibility of realising self-accelerated expansion of the Universe taking into account the vector components of a massive graviton. The effective action in the decoupling limit contains an infinite number of terms, once the vector degrees of freedom are included. These can be re-summed in physically interesting situations, which result in non-polynomial couplings between the scalar and vector modes. We show there are self-accelerating background solutions for this effective action, with the possibility of having a non-trivial profile for the vector fields. We then study fluctuations around these solutions and show that there is always a ghost, if a background vector field is present. When the background vector field is switched off, the ghost can be avoided, at the price of entering into a strong coupling regime, in which the vector fluctuations have vanishing kinetic terms. Finally we show that the inclusion of a bare cosmological constant does not change the previous conclusions and it does not lead to a ghost mode in the absence of a background vector field.