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The existence (and abundance) of primordial black holes (PBHs) is governed by the power spectrum of primordial perturbations generated during inflation. So far no PBHs have been observed, and instead, increasingly stringent bounds on their existence at different scales have been obtained. Up until recently, this has been exploited in attempts to constrain parts of the inflationary power spectrum that are unconstrained by cosmological observations. We first point out that the simple translation of the PBH non-observation bounds into constraints on the primordial power spectrum is inaccurate as it fails to include realistic aspects of PBH formation and evolution. We then demonstrate, by studying two examples of uncertainties from the effects of critical and non-spherical collapse, that even though they may seem small, they have important implications for the usefulness of the constraints. In particular, we point out that the uncertainty induced by non-spherical collapse may be much larger than the difference between particular bounds from PBH non-observations and the general maximum cap stemming from the condition Omega <= 1 on the dark-matter density in the form of PBHs. We therefore make the cautious suggestion of applying only the overall maximum dark-matter constraint to models of early Universe, as this requirement seems to currently provide a more reliable constraint, which better reflects our current lack of detailed knowledge of PBH formation. These, and other effects, such as merging, clustering and accretion, may also loosen constraints from non-observations of other primordial compact objects such as ultra-compact minihalos of dark matter.

Certain inflationary models as well as realisations of phase transitions in the early Universe predict the formation of primordial black holes. For most mass ranges, the fraction of matter in the form of primordial black holes is limited by many different observations on various scales. Primordial black holes are assumed to be formed when overdensities that cross the horizon have Schwarzschild radii larger than the horizon. Traditionally it was therefore assumed that primordial black-holemasses were equal to the horizon mass at their time of formation. However, detailed calculations of their collapse show that primordial black holes formed at each point in time should rather form a spectrum of different masses, obeying critical scaling. Though this has been known for more than 15 years, the effect of this scaling behaviour is largely ignored when considering predictions for primordial black-hole mass spectra. In this paper we consider the critical collapse scaling for a variety of models which produce primordial black holes, and find that it generally leads to a shift, broadening and an overall decrease of the mass contained in primordial black holes. This effect is model and parameter dependent and cannot be contained by a constant rescaling of the spectrum; it can become important and should be taken into account when comparing to observational constraints.

We reinvestigate gravitational ellipsoidal collapse with special focus on its impact on primordial black hole formation. We start with the results for the collapse threshold in the case of ellipsoidal collapse in the context of structure formation, and show heuristically that a similar functional form for the threshold should be expected in the case of primordial black hole formation. For a generic model we apply this to demonstrate that the abundance and energy density of the produced primordial black holes can be significantly decreased when the nonsphericity of the overdensities is taken into account. Further numerical study of this phenomenon may be crucial in order to produce reliable predictions for primordial black hole abundances from inflationary models.

The possibility that the dark matter comprises primordial black holes (PBHs) is considered, with particular emphasis on the currently allowed mass windows at 10(16)-10(17) g, 10(20)-10(24) g and 1-10(3)M(circle dot) The Planck mass relics of smaller evaporating PBHs are also considered. All relevant constraints (lensing, dynamical, large-scale structure and accretion) are reviewed and various effects necessary for a precise calculation of the PBH abundance (non-Gaussianity, nonsphericity, critical collapse and merging) are accounted for. It is difficult to put all the dark matter in PBHs if their mass function is monochromatic but this is still possible if the mass function is extended, as expected in many scenarios. A novel procedure for confronting observational constraints with an extended PBH mass spectrum is therefore introduced. This applies for arbitrary constraints and a wide range of PBH formation models and allows us to identify which model-independent conclusions can be drawn from constraints over all mass ranges. We focus particularly on PBHs generated by inflation, pointing out which effects in the formation process influence the mapping from the inflationary power spectrum to the PBH mass function. We then apply our scheme to two specific inflationary models in which PBHs provide the dark matter. The possibility that the dark matter is in intermediate-mass PBHs of 1-10(3)M(circle dot) is of special interest in view of the recent detection of black-hole mergers by LIGO. The possibility of Planck relics is also intriguing but virtually untestable.

We review the paradigm of eternal inflation in the light of the recently proposed corpuscular picture of space-time. Comparing the strength of the average fluctuation of the field up its potential with that of quantum depletion, we show that the latter can be dominant. We then study the full respective distributions in order to show that the fraction of the space-time which has an increasing potential is always below the eternal-inflation threshold. We prove that for monomial potentials eternal inflaton is excluded. This is likely to hold for other models as well.

Primordial black holes are studied in the Bose-Einstein condensate description of space-time. The question of baryon-number conservation is investigated with emphasis on the possible formation of bound states of the system's remaining captured baryons. This leads to distinct predictions both for the formation time, which for the naively natural assumptions is shown to lie between 10(-12) s and 10(12) s after the big bang, and for the remnant's mass, yielding approximately 3 x 10(23) kg in the same scheme. The consequences for astrophysically formed black holes are also considered.