Evolution of density perturbations through cosmological phase transitions

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Abstract
We study the evolution of energy density perturbations through a "new inflationary" phase transition using the gauge-invariant formalism developed by Bardeen. Pre-existing perturbations on spatial scales larger than the Hubble radius at the onset of the transition are expanded to very large sizes, but enter the "horizon" during the subsequent radiation-dominated era with an amplitude un-changed by the occurrence of the transition. Since inflation simply postpones the epoch at which such perturbations enter the "horizon," long-wavelength perturbations present prior to a long de Sitter phase would still be present today, but on unobservably large scales. We discuss the relevance of this result to cosmological scenarios with multiple phase transitions, and to the conjecture that inflationary models result in a universe whose present state is locally insensitive to initial conditions.