Tracking Pre-inflation Era from density perturbation spectra

TL;DR

This paper investigates the pre-inflation era dominated by radiation and curvature, deriving exact scalar field solutions and showing how these conditions influence the primordial power spectrum, especially on super-horizon scales.

Contribution

It provides exact solutions for scalar fields in a pre-inflation era with radiation and curvature, revealing their impact on the primordial power spectrum.

Findings

Power spectrum is nearly flat on sub-horizon scales.

Deviations from flatness occur on super-horizon scales due to pre-inflation conditions.

Power spectrum is sensitive to radiation and curvature in the pre-inflation era.

Abstract

One of the great triumphs of the inflationary model is the prediction of the flat power spectrum of the CMB fluctuation. The prediction is based on the assumption of the de-Sitter vacuum in the past infinity. However, the true past infinity of the inflation is expected to be dominated by radiation and curvature of the space. We consider pre-inflation era as dominated by radiation and curvatures as well as inflation potential. We derive the exact solutions for the scalar fields in this era and find a exact power spectra caused by the inflaton vacuum fluctuation. We show that the power spectrum is almost flat for sub-horizon scale and deviates from flat for very high super-horizon fluctuation, which is quite sensitive to the radiation and the curvature in the pre-inflation era.