Cosmological perturbations in inflationary-universe models

Abstract

We study the growth of energy-density perturbations in inflationary-universe models, applying an extension of Bardeen's gauge-invariant framework derived in a previous paper. The complete analysis is exemplified in the case of the ''new inflationary universe'' of Linde and Albrecht and Steinhardt. For this model we obtain the following result: the amplitude of energy-density fluctuations at horizon crossing is of order 50, far too large to match with the usual pictures of galaxy formation. Our result agrees with other published analyses. We conclude that the amplification of energy-density perturbations is determined by the change in the equation of state between initial and final Hubble radius crossing. It is, however, independent of the phase structure between the two crossings. In particular, it is independent of the reheating mechanism. We also derive a simple formula which describes the complete evolution of perturbations outside the horizon whenever entropy and anisotropic stress perturbations are unimportant. Finally, we comment on previous published methods and discuss their limitations.