Sound Speed of Primordial Fluctuations in Supergravity Inflation

TL;DR

This paper links the sound speed of primordial fluctuations in supergravity inflation to geometric and mass parameters, constraining models with potential non-Gaussianity based on observational data.

Contribution

It derives a new inequality relating sound speed, curvature tensor, and mass ratio in supergravity inflation, connecting theory with observational constraints.

Findings

The sound speed c_s cannot be much smaller than 0.4 unless specific conditions are met.

Large non-Gaussianity would impose severe constraints on supergravity inflation models.

The inequality provides a testable link between supergravity parameters and primordial non-Gaussianity.

Abstract

We study the realization of slow-roll inflation in $\mathcal N = 1$ supergravities where inflation is the result of the evolution of a single chiral field. When there is only one flat direction in field space, it is possible to derive a single-field effective field theory parametrized by the sound speed $c_s$ at which curvature perturbations propagate during inflation. The value of $c_s$ is determined by the rate of bend of the inflationary path resulting from the shape of the $F$-term potential. We show that $c_s$ must respect an inequality that involves the curvature tensor of the Kahler manifold underlying supergravity, and the ratio $M/H$ between the mass $M$ of fluctuations ortogonal to the inflationary path, and the Hubble expansion rate $H$. This inequality provides a powerful link between observational constraints on primordial non-Gaussianity and information about the $\mathcal N = 1$ supergravity responsible for inflation. In particular, the inequality does not allow for suppressed values of $c_s$ (values smaller than $c_s \sim 0.4$) unless (a) the ratio $M/H$ is of order 1 or smaller, and (b) the fluctuations of mass $M$ affect the propagation of curvature perturbations by inducing on them a nonlinear dispersion relation during horizon crossing. Therefore, if large non-Gaussianity is observed, supergravity models of inflation would be severely constrained.