On cosmic inflation in vector field theories

TL;DR

This paper examines the viability of Abelian vector inflation models, focusing on the ghost issue and stability conditions, and suggests exploring Lorentz-violating modifications for potential improvements.

Contribution

It analyzes the longitudinal ghost problem in Lorentz-invariant vector inflation theories and discusses conditions to avoid instabilities, proposing Lorentz-violating modifications as a promising direction.

Findings

Classical solution by Larry Ford is essentially unique for Lorentz-invariant models.

Avoiding gradient instability requires additional conditions on the potential.

Lorentz-violating modifications may offer viable alternatives.

Abstract

We investigate the longitudinal ghost issue in Abelian vector inflation. It turns out that, within the class of Lorentz-invariant vector field theories with three degrees of freedom and without any extra (scalar) fields, the possibilities are essentially exhausted by the classical solution due to Larry Ford with an extremely flat potential which doesn't feel the fast roll of its argument. And, moreover, one needs to fulfil an extra condition on that potential in order to avoid severe gradient instability. At the same time, some Lorentz-violating modifications are worth to be explored.