General conditions for scale-invariant perturbations in an expanding universe

TL;DR

This paper explores the conditions under which expanding universe models can produce scale-invariant curvature perturbations, highlighting the necessity of acceleration, superluminal sound speed, or super-Planckian energy densities.

Contribution

It establishes the minimal conditions needed for scale-invariant perturbations in expanding cosmologies with variable sound speed, extending previous understanding.

Findings

Accelerating expansion enables scale-invariant perturbations.

Superluminal sound speed can produce the desired spectrum.

Super-Planckian energy densities are also a viable condition.

Abstract

We investigate the general properties of expanding cosmological models which generate scale-invariant curvature perturbations in the presence of a variable speed of sound. We show that in an expanding universe, generation of a super-Hubble, nearly scale-invariant spectrum of perturbations over a range of wavelengths consistent with observation requires at least one of three conditions: (1) accelerating expansion, (2) a speed of sound faster than the speed of light, or (3) super-Planckian energy density.