Bj. Carr et al., BLACK-HOLE RELICS AND INFLATION - LIMITS ON BLUE PERTURBATION SPECTRA, Physical review. D. Particles and fields, 50(8), 1994, pp. 4853-4867
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.