Evolution of a Primordial Black Hole Population

We reconsider in this work the effects of an energy absorption term in the evolution of primordial black holes (hereafter PBHs) in the several epochs of the Universe. A critical mass is introduced as a boundary between the accreting and evaporating regimes of the PBHs. We show that the growth of PBHs is negligible in the Radiation-dominated Era due to scarcity of energy density supply from the expanding background, in agreement with a previous analysis by Carr and Hawking, but that nevertheless the absorption term is large enough for black holes above the critical mass to preclude their evaporation until the universe has cooled sufficiently. The effects of PBH motion are also discussed: the Doppler effect may give rise to energy accretion in black-holes with large peculiar motions relative to background. We discuss how cosmological constraints are modified by the introduction of the critical mass since that PBHs above it do not disturb the CMBR. We show that there is a large range of admissible masses for PBHs above the critical mass but well below the cosmological horizon. Finally we outline a minimal kinetic formalism, solved in some limiting cases, to deal with more complicated cases of PBH populationsComment: RevTex file, 8 pp., 3 .ps figures available upon request from [email protected]

Viability of primordial black holes as short period gamma-ray bursts

It has been proposed that the short period gamma-ray bursts, which occur at a rate of $\sim 10 {\rm yr^{-1}}$, may be evaporating primordial black holes (PBHs). Calculations of the present PBH evaporation rate have traditionally assumed that the PBH mass function varies as $M_{{\rm BH}}^{-5/2}$. This mass function only arises if the density perturbations from which the PBHs form have a scale invariant power spectrum. It is now known that for a scale invariant power spectrum, normalised to COBE on large scales, the PBH density is completely negligible, so that this mass function is cosmologically irrelevant. For non-scale-invariant power spectra, if all PBHs which form at given epoch have a fixed mass then the PBH mass function is sharply peaked around that mass, whilst if the PBH mass depends on the size of the density perturbation from which it forms, as is expected when critical phenomena are taken into account, then the PBH mass function will be far broader than $M_{{\rm BH}}^{-5/2}$. In this paper we calculate the present day PBH evaporation rate, using constraints from the diffuse gamma-ray background, for both of these mass functions. If the PBH mass function has significant finite width, as recent numerical simulations suggest, then it is not possible to produce a present day PBH evaporation rate comparable with the observed short period gamma-ray burst rate. This could also have implications for other attempts to detect evaporating PBHs.Comment: 5 pages, 2 figures, version to appear in Phys. Rev. D with additional reference

Bounds from Primordial Black Holes with a Near Critical Collapse Initial Mass Function

Recent numerical evidence suggests that a mass spectrum of primordial black holes (PBHs) is produced as a consequence of near critical gravitational collapse. Assuming that these holes formed from the initial density perturbations seeded by inflation, we calculate model independent upper bounds on the mass variance at the reheating temperature by requiring the mass density not exceed the critical density and the photon emission not exceed current diffuse gamma-ray measurements. We then translate these results into bounds on the spectral index n by utilizing the COBE data to normalize the mass variance at large scales, assuming a constant power law, then scaling this result to the reheating temperature. We find that our bounds on n differ substantially (\delta n > 0.05) from those calculated using initial mass functions derived under the assumption that the black hole mass is proportional to the horizon mass at the collapse epoch. We also find a change in the shape of the diffuse gamma-ray spectrum which results from the Hawking radiation. Finally, we study the impact of a nonzero cosmological constant and find that the bounds on n are strengthened considerably if the universe is indeed vacuum-energy dominated today.Comment: 24 pages, REVTeX, 5 figures; minor typos fixed, two refs added, version to be published in PR

Probing the Galactic Dark Matter Mass Funtion Using Microlensing and Direct Searches

If compact baryonic objects contribute significantly to the dark matter in our Galaxy, their mass function will present vital clues for galaxy formation theories and star formation processes in the early Universe. Here we discuss what one might expect to learn about the mass function of Galactic dark matter from microlensing and from direct searches in the infrared and optical wavebands. Current microlensing results from the \eros\/ collaboration already constrain halo mass functions which extend below 10^{-4}~\sm, whilst recent \hst\/ observations place strong constraints on disc and halo dark matter mass functions extending above 0.1~\sm. Infrared observations should either detect or constrain objects larger than 0.01~\sm in the near future. Objects below 0.01~\sm should be detectable through microlensing, although the prospects of determining their mass function depend critically on a number of factors.Comment: uuencoded, gzipped postscript file (4 pages). Postscript file (massfunc.ps) can also be obtained via anonymous ftp to 138.37.48.101 in dir /pub/ejk/ir+lens. Based on a talk presented at the conference "Trends in Astroparticle Physics", Stockholm, Sweden, 22-25 September. To be published in Nucl. Phys. B Proceedings Supplemen

Uniqueness of Self-Similar Asymptotically Friedmann-Robertson-Walker Spacetime in Brans-Dicke theory

We investigate spherically symmetric self-similar solutions in Brans-Dicke theory. Assuming a perfect fluid with the equation of state $p=(\gamma-1)\mu (1 \le \gamma<2)$, we show that there are no non-trivial solutions which approach asymptotically to the flat Friedmann-Robertson-Walker spacetime if the energy density is positive. This result suggests that primordial black holes in Brans-Dicke theory cannot grow at the same rate as the size of the cosmological particle horizon.Comment: Revised version, 4 pages, no figures, Revtex, accepted for publication in Physical Review

Primordial black holes in braneworld cosmologies: Formation, cosmological evolution and evaporation

We consider the population evolution and evaporation of primordial black holes in the simplest braneworld cosmology, Randall-Sundrum type II. We demonstrate that black holes forming during the high-energy phase of this theory (where the expansion rate is proportional to the density) have a modified evaporation law, resulting in a longer lifetime and lower temperature at evaporation, while those forming in the standard regime behave essentially as in the standard cosmology. For sufficiently large values of the AdS radius, the high-energy regime can be the one relevant for primordial black holes evaporating at key epochs such as nucleosynthesis and the present. We examine the formation epochs of such black holes, and delimit the parameter regimes where the standard scenario is significantly modified.Comment: 9 pages RevTeX4 file with four figures incorporated, minor changes to match published versio

Black hole gas in the early universe

We consider the early universe at temperatures close to the fundamental scale of gravity (M_D << M_Planck) in models with extra dimensions. At such temperatures a small fraction of particles will experience transplanckian collisions that may result in microscopic black holes (BHs). BHs colder than the environment will gain mass, and as they grow their temperature drops further. We study the dynamics of a system (a black hole gas) defined by radiation at a given temperature coupled to a distribution of BHs of different mass. Our analysis includes the production of BHs in photon-photon collisions, BH evaporation, the absorption of radiation, collisions of two BHs to give a larger one, and the effects of the expansion. We show that the system may follow two different generic paths depending on the initial temperature of the plasma.Comment: 17 pages, version to appear in JCA

The Height of a Giraffe

A minor modification of the arguments of Press and Lightman leads to an estimate of the height of the tallest running, breathing organism on a habitable planet as the Bohr radius multiplied by the three-tenths power of the ratio of the electrical to gravitational forces between two protons (rather than the one-quarter power that Press got for the largest animal that would not break in falling over, after making an assumption of unreasonable brittleness). My new estimate gives a height of about 3.6 meters rather than Press's original estimate of about 2.6 cm. It also implies that the number of atoms in the tallest runner is very roughly of the order of the nine-tenths power of the ratio of the electrical to gravitational forces between two protons, which is about 3 x 10^32.Comment: 12 pages, LaTe

Spherically Symmetric, Self-Similar Spacetimes

Self-similar spacetimes are of importance to cosmology and to gravitational collapse problems. We show that self-similarity or the existence of a homothetic Killing vector field for spherically symmetric spacetimes implies the separability of the spacetime metric in terms of the co-moving coordinates and that the metric is, uniquely, the one recently reported in [cqg1]. The spacetime, in general, has non-vanishing energy-flux and shear. The spacetime admits matter with any equation of state.Comment: Submitted to Physical Review Letter

Homothetic Self-Similar Solutions of the Three-Dimensional Brans-Dicke Gravity

All homothetic self-similar solutions of the Brans-Dicke scalar field in three-dimensional spacetime with circular symmetry are found in closed form.Comment: latex, five pages, without figur