Just enough inflation: power spectrum modifications at large scales

TL;DR

This paper investigates how limited-duration inflation models affect the CMB power spectrum at large scales, revealing universal features like power loss or enhancement depending on pre-inflationary conditions.

Contribution

It provides a systematic, model-independent analysis of non-slow-roll pre-inflationary backgrounds and their impact on large-scale CMB anisotropies.

Findings

Most pre-inflationary backgrounds cause power loss at large scales.

Different epochs can lead to power enhancement or suppression.

Results are consistent with observed CMB anomalies.

Abstract

We show that models of `just enough' inflation, where the slow-roll evolution lasted only $50-60$ e-foldings, feature modifications of the CMB power spectrum at large angular scales. We perform a systematic and model-independent analysis of any possible non-slow-roll background evolution prior to the final stage of slow-roll inflation. We find a high degree of universality since most common backgrounds like fast-roll evolution, matter or radiation-dominance give rise to a power loss at large angular scales and a peak together with an oscillatory behaviour at scales around the value of the Hubble parameter at the beginning of slow-roll inflation. Depending on the value of the equation of state parameter, different pre-inflationary epochs lead instead to an enhancement of power at low-$\ell$, and so seem disfavoured by recent observational hints for a lack of CMB power at $\ell\lesssim 40$. We also comment on the importance of initial conditions and the possibility to have multiple pre-inflationary stages.