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 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.
