Primordial fluctuations without scalar fields

TL;DR

This paper explores whether hydrodynamical matter with variable equation of state and sound speed can generate primordial fluctuations, offering alternatives to scalar field models and identifying conditions for scale-invariance in different universe scenarios.

Contribution

It demonstrates that hydrodynamical models with specific variable parameters can produce scale-invariant fluctuations, providing new insights beyond scalar field-based theories.

Findings

Power-law models are generally ruled out for expanding universes.

A phase transition in sound speed can produce scale-invariant fluctuations with thermal initial conditions.

In contracting universes, only a specific $w \\propto \\ep_0^2$ model yields scale-invariance.

Abstract

We revisit the question of whether fluctuations in hydrodynamical, adiabatical matter could explain the observed structures in our Universe. We consider matter with variable equation of state $w=p_0/\ep_0$ and a concomitant (under the adiabatic assumption) density dependent speed of sound, $c_s$. We find a limited range of possibilities for a set up when modes start inside the Hubble radius, then leaving it and freezing out. For expanding Universes, power-law $w(\ep_0)$ models are ruled out (except when $c_s^2\propto w \ll 1$, requiring post-stretching the seeded fluctuations); but sharper profiles in $c_s$ do solve the horizon problem. Among these, a phase transition in $c_s$ is notable for leading to scale-invariant fluctuations if the initial conditions are thermal. For contracting Universes all power-law $w(\ep_0)$ solve the horizon problem, but only one leads to scale-invariance: $w\propto \ep_0^2$ and $c_s\propto \ep_0$. This model bypasses a number of problems with single scalar field cyclic models (for which $w$ is large but constant).