Non-adiabatic primordial fluctuations

TL;DR

This paper develops a general formalism for analyzing mixed isocurvature and adiabatic primordial fluctuations, deriving new conserved quantities and applying the framework to a Chaplygin gas model with scale-invariant solutions.

Contribution

It introduces a comprehensive approach to study mixed primordial perturbations, deriving second-order actions and conserved quantities at a high level of generality.

Findings

Discovered a new conserved super-horizon quantity.

Related the new conserved quantity to the adiabatic curvature perturbation.

Found two scale-invariant solutions in a Chaplygin gas-like model.

Abstract

We consider general mixtures of isocurvature and adiabatic cosmological perturbations. With a minimal assumption set consisting of the linearized Einstein equations and a primordial perfect fluid we derive the second-order action and its curvature variables. We also allow for varying equation of state and speed of sound profiles. The derivation is therefore carried out at the same level of generality that has been achieved for adiabatic modes before. As a result we find a new conserved super-horizon quantity and relate it to the adiabatically conserved curvature perturbation. Finally we demonstrate how the formalism can be applied by considering a Chaplygin gas-like primordial matter model, finding two scale-invariant solutions for structure formation.