Gravitational Waves and Scalar Perturbations from Spectator Fields

TL;DR

This work analyzes a covariant spectator field with a low sound speed during inflation to assess its impact on gravitational wave production. By modeling σ with a P(X) Lagrangian and a non-minimal derivative coupling to gravity, the authors compute second-order sourced tensor and scalar perturbations, finding that the tensor-to-scalar ratio r no longer directly tracks the inflationary H but becomes highly sensitive to c_s. They identify regimes where scalar sourcing can dominate, potentially enhancing r only within constrained parameter ranges, and highlight the crucial role of non-Gaussianity constraints. The results demonstrate that GW signals do not unambiguously fix the inflationary energy scale in the presence of spectator-field sources, motivating further exploration of covariant formulations and observational signatures.

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 $σ$ with a sound speed $c_{s} \ll 1$ acts as a source for gw during inflation. In our formulation $σ$ 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 $σ$ 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.