Just enough inflation: power spectrum modifications at large scales

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 inflation. 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 ℓlesssim 40. We also comment on the importance of initial conditions and the possibility to have multiple pre-inflationary stages