Just enough inflation: Power spectrum modifications at large scales

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 analytic analysis in the limit of a sudden transition between any possible non-slow-roll background evolution and 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 inati inflation on. Depending on the value of the equation of state parameter, different pre-inflationary epochs lead instead to an enhancement of power at low-l, and so seem disfavoured by recent observational hints for a lack of CMB power at l≤40. We also comment on the importance of initial conditions and the possibility to have multiple pre-inflationary stages.