Scalar Perturbations at the Reheating Phase in a New Inflationary Universe

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Abstract
In order to analyze the behaviors of energy density perturbations and the perturbation of classical scalar field in a new inflationary universe, we solved their coupled equations, which are due to Sasaki’s extension of Bardeen’s gauge-invariant formalism for gravitational instability. We integrated from an initial time at the rolling phase, when the size of perturbations corresponding to present galaxies far exceeded the horizon length, to a final time when reheating was over and radiation was dominant. The relative density perturbations at the later time of horizon crossing are much smaller (by a factor 10-5) than the values (∼50) in the previous results by Bardeen et al. and others, and can be consistent with the value ∼10-4 which may be appropriate to galaxy formation. Because of this distinction, it is concluded that the scalar field perturbation plays and important role to raise the density perturbation at the reheating phase.

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