Gravitational waves in vector inflation

TL;DR

This paper analyzes gravitational waves in vector inflation models, deriving their behavior and stability, and identifies conditions under which tensor modes are stable or decay rapidly, affecting their detectability in the CMB.

Contribution

It derives the tensor perturbation action in vector inflation and clarifies stability conditions, highlighting differences between large and small field models.

Findings

Tachyonic instabilities are common in large field models.

Small field inflation models are stable under slow-roll conditions.

Some models predict rapid decay of gravitational waves, leading to no tensor modes in the CMB.

Abstract

We discuss the gravitational waves (GW) in the context of vector inflation. We derive the action for tensor perturbations and find that tachyonic instabilities are present in most (but not all) of the inflationary models with large fields. In contrast, the stability of the small field inflation ($A_{\mu}A^{\mu}\ll\frac{1}{N}$) is ensured by the usual slow-roll conditions, where $N$ is the total number of fields. For example, the Coleman-Weinberg potential and the power-law inflation are always stable in the small fields limit with an approximately flat spectrum of GW. We also provide some examples which lead to a rapid decay of GW and predict the absence of tensor modes in the CMB.