What initial condition of inflation would suppress the large-scale CMB spectrum?

TL;DR

This paper investigates how different initial conditions of the universe's inflationary phase affect the large-scale CMB spectrum, finding that certain initial states can suppress or enhance the spectrum depending on the equation of state parameter.

Contribution

It provides a detailed analysis of how initial vacuum states in various inflationary eras influence the large-scale CMB spectrum, clarifying conflicting previous conclusions.

Findings

Large-scale spectrum suppressed with initial adiabatic vacuum in super-inflation ($w < -1$) or positive-pressure ($w > 0$) eras.

No causal mechanism to establish vacuum in super-inflation ($w < -1$) era.

Two-stage inflation model results agree with single-field analysis.

Abstract

There is an apparent power deficit relative to the $\Lambda$CDM prediction of the CMB spectrum at large scales, which, though not yet statistically significant, persists from WMAP to Planck data. Proposals that invoke some form of initial condition for the inflation have been made to address this apparent power suppression, albeit with conflicting conclusions. By studying the curvature perturbations of a scalar field in the FLRW universe parameterized by the equation of state parameter $w$, we find that the large-scale spectrum at the end of inflation reflects the super-horizon spectrum of the initial state. The large-scale spectrum is suppressed if the universe begins with the adiabatic vacuum in a super-inflation ($w < -1$) or positive-pressure ($w > 0$) era. In the latter case, there is however no causal mechanism to establish the initial adiabatic vacuum. On the other hand, as long as the universe begins with the adiabatic vacuum in an era with $-1 < w < 0$, even if there exists an intermediate positive-pressure era, the large-scale spectrum would be enhanced rather than suppressed. We further calculate the spectrum of a two-stage inflation model with a two-field potential and show that the result agrees with that obtained from the ad hoc single-field analysis.