Beyond the Simplest Inflationary Cosmological Models
  Though predictions of the simplest inflationary cosmological models with cold dark matter, flat space and approximately flat initial spectrum of adiabatic perturbations are remarkably close to observational data, we have to go beyond them and to introduce new physics not yet discovered in laboratories to account for all data. Two extensions of these models which seem to be the most actual at present time are discussed. The first one is the possibility that we are living at the beginning of a new inflation-like era. Then classical cosmological tests, like the luminosity distance or the angular size of distant objects as functions of redshift, as well as the behaviour of density perturbations in a dustlike matter component including baryons as a function of redshift, can provide information sufficient for the unambiguous determination of an effective potential of a corresponding present inflaton scalar field. The second, unrelated extension is a possibility of broken-scale-invariant cosmological models which have localized steps or spikes in the primordial perturbation spectrum. These features can be produced by fast phase transitions in physical fields other than an inflaton field in the early Universe during inflation and not far from the end of it. At present, it seems that the only scale in the spectrum around which we might see something of this type is $k=0.05 h Mpc^{-1}$. 
A.A. Starobinsky