Cosmological perturbations of a perfect fluid and noncommutative variables

TL;DR

This paper develops an action-based approach to linear cosmological perturbations of perfect fluids, revealing noncommutative properties of perturbation fields and implications for measurement and stability under certain conditions.

Contribution

It introduces an action formalism for fluid perturbations that includes noncommutative variables and analyzes their quantum properties and physical implications.

Findings

Perturbation fields exhibit noncommutativity similar to charged particles in magnetic fields.

Local curvature and pressure perturbations cannot be measured simultaneously.

Ghosts appear when the null energy condition is violated.

Abstract

We describe the linear cosmological perturbations of a perfect fluid at the level of an action, providing thus an alternative to the standard approach based only on the equations of motion. This action is suited not only to perfect fluids with a barotropic equation of state, but also to those for which the pressure depends on two thermodynamical variables. By quantizing the system we find that (1) some perturbation fields exhibit a noncommutativity quite analogous to the one observed for a charged particle moving in a strong magnetic field, (2) local curvature and pressure perturbations cannot be measured simultaneously, (3) ghosts appear if the null energy condition is violated.