Initial condition of scalar perturbation in inflation

TL;DR

This paper derives a general formula for the power spectrum of scalar perturbations in inflation, considering various initial states, including non-Bunch-Davies states, and explores their effects in different cosmological scenarios.

Contribution

It introduces a formula for the power spectrum with arbitrary initial conditions and analyzes the impact of pre-inflationary radiation periods on scalar perturbations.

Findings

Scalar perturbations can originate from states other than Bunch-Davies.

The power spectrum exhibits oscillations when a radiation-dominated period precedes inflation.

Large enhancements in the power spectrum occur with significant breaks in inflation depending on the breaking time.

Abstract

A formula for the power spectrum of curvature perturbations having any initial conditions in inflation is obtained. Based on the physical conditions before inflation, the possibility exists that the initial state of scalar perturbations is not only the Bunch-Davies state, but also a more general state (a squeezed state). For example, the derived formula for the power spectrum is calculated using simple toy cosmological models. When there exists a radiation-dominated period before inflation, the behavior of the scalar perturbation is revealed not to vary greatly; however, from large scales to small scales the power spectrum of the curvature perturbations oscillates around the normal value. In addition, when inflation has a large break and the breaking time is a radiation- dominated period, a large enhancement is revealed to occur which depends on the length of the breaking time.