Gravitational Waves and Scalar Perturbations from Spectator Fields

TL;DR

This paper explores how a spectator scalar field with low sound speed during inflation can generate gravitational waves, disrupting the usual link between gravitational wave amplitude and the inflationary expansion rate.

Contribution

It introduces a covariant formulation of a spectator field mechanism with non-minimal gravity coupling, showing how it affects gravitational wave production during inflation.

Findings

Gravitational wave amplitude is highly sensitive to the sound speed of the spectator field.

The usual direct relation between tensor-to-scalar ratio and inflationary scale is broken.

Scalar and tensor fluctuations depend on the properties of the spectator field.

Abstract

The most conventional mechanism for gravitational waves (gw) production during inflation is the amplification of vacuum metric fluctuations. In this case the gw production can be uniquely related to the inflationary expansion rate $H$. For example, a gw detection close to the present experimental limit (tensor-to-scalar ratio $r \sim 0.1$) would indicate an inflationary expansion rate close to $10^{14} \, {\rm GeV}$. This conclusion, however, would be invalid if the observed gw originated from a different source. We construct and study one of the possible covariant formulations of the mechanism suggested in [43], where a spectator field $\sigma$ with a sound speed $c_{s} \ll 1$ acts as a source for gw during inflation. In our formulation $\sigma$ is described by a so-called $P(X)$ Lagrangian and a non-minimal coupling to gravity. This field interacts only gravitationally with the inflaton, which has a standard action. We compute the amount of scalar and tensor density fluctuations produced by $\sigma$ and find that, in our realization, $r$ is not enhanced with respect to the standard result but it is strongly sensitive to $c_s$, thus breaking the direct $r \leftrightarrow H$ connection.