Further evidences for a generic Universe

Recently it was argued that an inflationary potential yielding power spectra characterized by a scale-invariant tensorial spectral index and a weakly scale-dependent scalar spectral index might account for a generic large-scale structure formation in the multiverses scenario of eternal inflation. Here it is shown that this statement remains true if the tensorial index is allowed to slowly vary in a wide range of angular scales. In the cases analyzed in this paper, the scalar index also slightly depends on the scales. Therefore, the production of closely resembling each other universes seems to be a common feature of inflationary scenarios with weakly scale-dependent spectral indices. With power-law inflation as the extreme case, this is the class of scenarios which may give the best fit to near future CMB observations.