Perturbations in a holographic universe and in other stiff fluid cosmologies

We examine the generation and evolution of perturbations in a universe dominated by a fluid with stiff equation of state p=ρ. The recently proposed holographic universe is an example of such a model. We compute the spectrum of scalar and tensor perturbations, without relying on a microphysical description of the p=ρ fluid. The spectrum is scale invariant deep inside the Hubble horizon. In contrast, infrared perturbations that enter the Hubble horizon during the stiff fluid dominated (holographic) phase yield oscillatory and logarithmic terms in the power spectrum. We show that vector perturbations grow during the stiff fluid dominated epoch and may result in a turbulent and anisotropic universe at the end of the holographic phase. Therefore, the required period of inflation following the holographic phase cannot be much shorter than that required in standard inflationary models