An analysis of cosmological perturbations in hydrodynamical and field representations

Density fluctuations of fluids with negative pressure exhibit decreasing ti me behaviour in the long-wavelength limit, but are strongly unstable in the small-wavelength limit when a hydrodynamical approach is used. On the othe r hand, the corresponding gravitational waves are well behaved. We verify t hat the instabilities present in density fluctuations are due essentially t o the hydrodynamical representation: if we turn to a field representation t hat leads to the same background behaviour, the instabilities are no longer present. In the long-wavelength limit, both approaches give the same resul ts. We also show that this inequivalence between background and perturbativ e level is a feature of a negative pressure fluid. When the fluid has posit ive pressure, the hydrodynamical representation leads to the same behaviour as the field representation both at the background and perturbative levels .