Primordial black hole constraints in cosmologies with early matter domination

Moduli fields, a natural prediction of any supergravity and superstring-inspired supersymmetry theory, may lead to a prolonged period of matter domination in the early Universe. This can be observationally viable provided the moduli decay early enough to avoid harming nucleosynthesis. If primordial black holes form, they would be expected to do so before or during this matter dominated era. We examine the extent to which the standard primordial black hole constraints are weakened in such a cosmology. Permitted mass fractions of black holes at formation are of order $10^{-8}$, rather than the usual $10^{-20}$ or so. If the black holes form from density perturbations with a power-law spectrum, its spectral index is limited to $n \lesssim 1.3$, rather than the $n \lesssim 1.25$ obtained in the standard cosmology.Comment: 7 pages RevTeX file with four figures incorporated (uses RevTeX and epsf). Also available by e-mailing ARL, or by WWW at http://star-www.maps.susx.ac.uk/papers/infcos_papers.htm

Blue spectra and induced formation of primordial black holes

We investigate the statistical properties of primordial black hole (PBH) formation in the very early Universe. We show that the high level of inhomogeneity of the early Universe leads to the formation of the first generation PBHs. %The existence of these PBHs This causes later the appearance of a dust-like phase of the cosmological expansion. We discuss here a new mechanism for the second generation of PBH formation during the dust-like phase. This mechanism is based on the coagulation process. We demonstrate that the blue power spectrum of initial adiabatic perturbations after inflation leads to overproduction of primordial black holes with $10^9$g$\le M\le10^{15}$g if the power index is $n\ge1.2$.Comment: 16 pages, 2 figure

Supersymmetry and primordial black hole abundance constraints

We study the consequences of supersymmetry for primordial black hole (PBH) abundance constraints. PBHs with mass less than about 10^{11}g will emit supersymmetric particles when they evaporate. In most models of supersymmetry the lightest of these particles, the lightest supersymmetric particle (LSP), is stable and will hence survive to the present day. We calculate the limit on the initial abundance of PBHs from the requirement that the present day LSP density is less than the critical density. We apply this limit, along with those previously obtained from the effects of PBH evaporation on nucleosynthesis and the present day density of PBHs, to PBHs formed from the collpase of inflationary density perturbations, in the context of supersymmetric inflation models. If the reheat temperature after inflation is low, so as to avoid the overproduction of gravitinos and moduli, then the lightest PBHs which are produced in significant numbers will be evaporating around the present day and there are therefore no constraints from the effects of the evaporation products on nucleosynthesis or from the production of LSPs. We then examine models with a high reheat temperature and a subsequent period of thermal inflation. In these models avoiding the overproduction of LSPs limits the abundance of low mass PBHs which were previously unconstrained. Throughout we incorporate the production, at fixed time, of PBHs with a range of masses, which occurs when critical collapse is taken into account.Comment: 8 pages RevTeX file with 3 figures incorporated (uses RevTeX and epsf). Version to appear in Phys. Rev. D: minor change to calculation and added discussio

Constraints on the density perturbation spectrum from primordial black holes

We re-examine the constraints on the density perturbation spectrum, including its spectral index $n$, from the production of primordial black holes. The standard cosmology, where the Universe is radiation dominated from the end of inflation up until the recent past, was studied by Carr, Gilbert and Lidsey; we correct two errors in their derivation and find a significantly stronger constraint than they did, $n \lesssim 1.25$ rather than their 1.5. We then consider an alternative cosmology in which a second period of inflation, known as thermal inflation and designed to solve additional relic over-density problems, occurs at a lower energy scale than the main inflationary period. In that case, the constraint weakens to $n \lesssim 1.3$, and thermal inflation also leads to a `missing mass' range, $10^{18} g \lesssim M \lesssim 10^{26} g$, in which primordial black holes cannot form. Finally, we discuss the effect of allowing for the expected non-gaussianity in the density perturbations predicted by Bullock and Primack, which can weaken the constraints further by up to 0.05.Comment: 10 pages RevTeX file with four figures incorporated (uses RevTeX and epsf). Also available by e-mailing ARL, or by WWW at http://star-www.maps.susx.ac.uk/papers/infcos_papers.htm