Sound Speed of Primordial Fluctuations in Supergravity Inflation

We study the realization of slow-roll inflation in 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 N = 1 supergravity responsible for inflation. In particular, the inequality does not allow for suppressed values of cs (values smaller than c(s) = 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.