Effect of Pre-inflation Conditions on Scalar and Tensor Perturbations in Inflation

TL;DR

This paper investigates how initial conditions before inflation influence scalar and tensor perturbations, deriving formulas for power spectra and exploring implications for pre-inflationary models.

Contribution

It derives general formulae for power spectra under any initial conditions and applies them to simplified pre-inflationary models, assessing their observational differences.

Findings

Formulas for gravitational wave and curvature perturbation spectra derived.

Differences in spectral index and ratio depend on matching conditions.

Power spectrum of gravitational waves obtained for current observations.

Abstract

The effect of the initial conditions in inflation on scalar and tensor perturbations is investigated. Formulae for the power spectra of gravitational waves and curvature perturbations for any initial conditions in inflation are derived, and the ratio of scalar to tensor perturbations and spectral index are calculated. The formulation is applied to some simplified pre-inflationary cosmological models, and the differences of the ratio and spectral index are investigated with respect to two matching conditions. In addition, the present power spectrum of gravitational waves is derived. The proposed formulation is preliminarily shown to be a possible test of the appropriateness of a given pre-inflationary model.