BLACK-HOLE RELICS AND INFLATION - LIMITS ON BLUE PERTURBATION SPECTRA

Blue primordial power spectra have spectral index n > 1 and arise natu rally in the recently proposed hybrid inflationary scenario. An observ ational upper Limit op n is derived by normalizing the spectrum at the quadrupole scale and considering the possible overproduction of Planc k mass relies formed in the final stage of primordial black hole evapo ration. In the inflationary Universe with the maximum reheating temper ature compatible with the observed quadrupole anisotropy, the upper li mit is n = 1.4, but it is slightly weaker for lower reheat temperature s. This limit applies over 57 decades of mass and is therefore insensi tive to cosmic variance and any gravitational wave contribution to the quadrupole anisotropy. It is also independent of the dark matter cont ent of the Universe and therefore the bias parameter. In some circumst ances, there maybe an extended dustlike phase between the end of infla tion and reheating. In this case, primordial black holes form more abu ndantly and the upper limit is n = 1.3.