An analysis of cosmological perturbations in hydrodynamical and field representations

TL;DR

This paper compares hydrodynamical and field representations of cosmological perturbations, revealing that instabilities in density fluctuations are due to the hydrodynamical approach and are absent in the field representation, especially for negative pressure fluids.

Contribution

It demonstrates that the hydrodynamical approach introduces instabilities in negative pressure fluids, which are not present in the field representation, clarifying the differences at background and perturbative levels.

Findings

Hydrodynamical approach causes instabilities in negative pressure fluids.

Field representation removes these instabilities.

Both approaches agree in the long wavelength limit.

Abstract

Density fluctuations of fluids with negative pressure exhibit decreasing time behaviour in the long wavelength limit, but are strongly unstable in the small wavelength limit when a hydrodynamical approach is used. On the other hand, the corresponding gravitational waves are well behaved. We verify that the instabilities present in density fluctuations are due essentially to the hydrodynamical representation; if we turn to a field representation that lead to the same background behaviour, the instabilities are no more present. In the long wavelength limit, both approachs give the same results. We show also that this inequivalence between background and perturbative level is a feature of negative pressure fluid. When the fluid has positive pressure, the hydrodynamical representation leads to the same behaviour as the field representation both at the background and perturbative levels.