An analysis of cosmological perturbations in hydrodynamical and field representations

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 leads to the same background behaviour, the instabilities are no longer present. In the long-wavelength limit, both approaches give the same results. We also show that this inequivalence between background and perturbative level is a feature of a 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.