Mass Fraction Of Primordial Black Holes Research Articles

Primordial black holes and stochastic inflation beyond slow roll. Part I. Noise matrix elements

Primordial Black Holes (PBHs) may form in the early Universe, from the gravitational collapse of large density perturbations, generated by large quantum fluctuations during inflation. Since PBHs form from rare over-densities, their abundance is sensitive to the tail of the primordial probability distribution function (PDF) of the perturbations. It is therefore important to calculate the full PDF of the perturbations, which can be done non-perturbatively using the `stochastic inflation' framework. In single field inflation models generating large enough perturbations to produce an interesting abundance of PBHs requires violation of slow roll. It is therefore necessary to extend the stochastic inflation formalism beyond slow roll. A crucial ingredient for this are the stochastic noise matrix elements of the inflaton potential. We carry out analytical and numerical calculations of these matrix elements for a potential with a feature which violates slow roll and produces large, potentially PBH generating, perturbations. We find that the transition to an ultra slow-roll phase results in the momentum induced noise terms becoming larger than the field noise whilst each of them falls exponentially for a few e-folds. The noise terms then start rising with their original order restored, before approaching constant values which depend on the nature of the slow roll parameters in the post transition epoch. This will significantly impact the quantum diffusion of the coarse-grained inflaton field, and hence the PDF of the perturbations and the PBH mass fraction.

Impact of radiation from primordial black holes on the 21-cm angular-power spectrum in the dark ages

We investigate the impact of radiation from primordial black holes (PBHs), in the mass range of ${10}^{15}\ensuremath{\lesssim}{M}_{\mathrm{PBH}}\ensuremath{\lesssim}{10}^{17}\text{ }\text{ }\mathrm{g}$ and ${10}^{2}\ensuremath{\lesssim}{M}_{\mathrm{PBH}}\ensuremath{\lesssim}{10}^{4}{M}_{\ensuremath{\bigodot}}$, on the 21-cm angular-power spectrum in the dark ages. PBHs in the former mass range affect the 21-cm angular-power spectrum through the evaporation known as Hawking radiation, while the radiation from the accretion process in the latter mass range. In the dark ages, radiation from PBHs can increase the ionization fraction and temperature of the intergalactic medium, change the global 21-cm differential brightness temperature and then affect the 21-cm angular-power spectrum. Taking into account the effects of PBHs, we find that in the dark ages, $30\ensuremath{\lesssim}z\ensuremath{\lesssim}100$, the amplitude of the 21-cm angular-power spectrum is decreased depending on the mass and mass fraction of PBHs. We also investigate the potential constraints on the mass fraction of PBHs in the form of dark matter for the future radio telescope in lunar orbit or on the far side surface of the Moon.

Non-Gaussianity effects on the primordial black hole abundance for sharply-peaked primordial spectrum

We perturbatively study the effect of non-Gaussianities on the mass fraction of primordial black holes (PBHs) at the time of formation by systematically taking its effect into account in the one-point probability distribution function of the primordial curvature perturbation. We focus on the bispectrum and trispectrum and derive formulas that describe their effects on the skewness and kurtosis of the distribution function. Then considering the case of narrowly peaked spectra, we obtain simple formulas that concisely express the effect of the bi- and trispectra. In particular, together with the g NL and τ NL parameters of the trispectrum, we find that non-Gaussianity parameters for various types of the bispectrum are linearly combined to give an effective parameter, f NL eff, that determines the PBH mass fraction in the narrow spectral shape limit.

Press–Schechter primordial black hole mass functions and their observational constraints

ABSTRACT We present a modification of the Press–Schechter (PS) formalism to derive general mass functions for primordial black holes (PBHs), considering their formation as being associated with the amplitude of linear energy density fluctuations. To accommodate a wide range of physical relations between the linear and non-linear conditions for collapse, we introduce an additional parameter to the PS mechanism, and that the collapse occurs at either a given cosmic time, or as fluctuations enter the horizon. We study the case where fluctuations obey Gaussian statistics and follow a primordial power spectrum of broken power-law form with a blue spectral index for small scales. We use the observed abundance of supermassive black holes (SMBH) to constrain the extended mass functions taking into account dynamical friction. We further constrain the modified PS by developing a method for converting existing constraints on the PBH mass fraction, derived assuming monochromatic mass distributions for PBHs, into constraints applicable for extended PBH mass functions. We find that when considering well-established monochromatic constraints, there are regions in parameter space where all the dark matter can be made of PBHs. Of special interest is the region for the characteristic mass of the distribution ${\sim}10^2\, \mathrm{M}_\odot$, for a wide range of blue spectral indices in the scenario where PBHs form as they enter the horizon, where the linear threshold for collapse is of the order of the typical overdensities, as this is close to the black hole masses detected by LIGO, which are difficult to explain by stellar collapse.

Cusp-to-core transition in low-mass dwarf galaxies induced by dynamical heating of cold dark matter by primordial black holes

ABSTRACT We performed a series of high-resolution N-body simulations to examine whether dark matter candidates in the form of primordial black holes (PBHs) can solve the cusp–core problem in low-mass dwarf galaxies. If some fraction of the dark matter in low-mass dwarf galaxies consists of PBHs and the rest is cold dark matter, dynamical heating of the cold dark matter by the PBHs induces a cusp-to-core transition in the total dark matter profile. The mechanism works for PBHs in the 25–100 M⊙ mass window, consistent with the Laser Interferometer Gravitational-Wave Observatory (LIGO) detections, but requires a lower limit on the PBH mass fraction of 1 ${{\rm per\ cent}}$ of the total dwarf galaxy dark matter content. The cusp-to-core transition time-scale is between 1 and 8 Gyr. This time-scale is also a constant multiple of the relaxation time between cold dark matter particles and PBHs, which depends on the mass, the mass fraction, and the scale radius of the initial density profile of PBHs. We conclude that dark matter cores occur naturally in haloes composed of cold dark matter and PBHs, without the need to invoke baryonic processes.

Primordial black holes dark matter from inflection point models of inflation and the effects of reheating

We study the generation of primordial black holes (PBH) in a single field inflection point model of inflation wherein the effective potential is expanded up to the sextic order and the inversion symmetry is imposed such that only even powers are retained in the potential. Such a potential allows the existence of an inflection point which leads to a dynamical phase of ultra slow roll evolution, thereby causing an enhancement of the primordial perturbation spectrum at smaller scales. Working with a quasi-inflection point in the potential, we find that PBHs can be produced in our scenario in the asteroid-mass window with a nearly monochromatic mass fraction which can account for the total dark matter in the universe. For different choices of quasi-inflection points and other parameters of our model, we can also generate PBHs in higher mass windows but the primordial spectrum of curvature perturbations becomes strongly tilted at the CMB scales. Moreover, we study the effects of a reheating epoch after the end of inflation on the PBHs mass fraction and find that an epoch of a matter dominated reheating can shift the mass fraction to a larger mass window as well as increase their fractional contribution to the total dark matter even for the case of a monochromatic mass fraction.

Constraints on Earth-mass primordial black holes from OGLE 5-year microlensing events

We constrain the abundance of primordial black holes (PBH) using 2622 microlensing events obtained from 5-years observations of stars in the Galactic bulge by the Optical Gravitational Lensing Experiment (OGLE). The majority of microlensing events display a single or at least continuous population that has a peak around the light curve timescale $t_{\rm E}\simeq 20~{\rm days}$ and a wide distribution over the range $t_{\rm E}\simeq [1, 300]~{\rm days}$, while the data also indicates a second population of 6 ultrashort-timescale events in $t_{\rm E}\simeq [0.1,0.3]~{\rm days}$, which are advocated to be due to free-floating planets. We confirm that the main population of OGLE events can be well modeled by microlensing due to brown dwarfs, main sequence stars and stellar remnants (white dwarfs and neutron stars) in the standard Galactic bulge and disk models for their spatial and velocity distributions. Using the dark matter (DM) model for the Milky Way (MW) halo relative to the Galactic bulge/disk models, we obtain the tightest upper bound on the PBH abundance in the mass range $M_{\rm PBH}\simeq[10^{-6},10^{-3}]M_\odot$ (Earth-Jupiter mass range), if we employ null hypothesis that the OGLE data does not contain any PBH microlensing event. More interestingly, we also show that Earth-mass PBHs can well reproduce the 6 ultrashort-timescale events, without the need of free-floating planets, if the mass fraction of PBH to DM is at a per cent level, which is consistent with other constraints such as the microlensing search for Andromeda galaxy (M31) and the longer timescale OGLE events. Our result gives a hint of PBH existence, and can be confirmed or falsified by microlensing search for stars in M31, because M31 is towards the MW halo direction and should therefore contain a much less number of free-floating planets, even if exist, than the direction to the MW center.

Sensitivity of primordial black hole abundance on the reheating phase

We investigate the sensitivity of reheating history on the abundance of primordial black holes (PBHs). Contrary to the monochromatic case of mass fraction of PBH, reheating era with different e-folding and equation-of-state can have a substantial impact on the abundance of PBH with an extended mass fraction. We demonstrate explicitly this reheating sensitivity in an illustrative model of single field inflation with a quasi-inflection point, and find that both the peak position and amplitude of the extended mass fraction as well as the abundance of PBH in DM can vary by many orders of magnitude, which adds another layer of uncertainty on the PBH scenarios as dark matter.

Cosmological implications of primordial black holes

The possibility that a relevant fraction of the dark matter might be comprised of Primordial Black Holes (PBHs) has been seriously reconsidered after LIGO's detection of a ∼ 30 M⊙ binary black holes merger. Despite the strong interest in the model, there is a lack of studies on possible cosmological implications and effects on cosmological parameters inference. We investigate correlations with the other standard cosmological parameters using cosmic microwave background observations, finding significant degeneracies, especially with the tilt of the primordial power spectrum and the sound horizon at radiation drag. However, these degeneracies can be greatly reduced with the inclusion of small scale polarization data. We also explore if PBHs as dark matter in simple extensions of the standard ΛCDM cosmological model induces extra degeneracies, especially between the additional parameters and the PBH's ones. Finally, we present cosmic microwave background constraints on the fraction of dark matter in PBHs, not only for monochromatic PBH mass distributions but also for popular extended mass distributions. Our results show that extended mass distribution's constraints are tighter, but also that a considerable amount of constraining power comes from the high-ℓ polarization data. Moreover, we constrain the shape of such mass distributions in terms of the correspondent constraints on the PBH mass fraction.

Moduli constraints on primordial black holes

The amount of late decaying massive particles (e.g., gravitinos, moduli) produced in the evaporation of primordial black holes (PBHs) of mass M BH ≲10 9 g is calculated. Limits imposed by big-bang nucleosynthesis on the abundance of these particles are used to constrain the initial PBH mass fraction β (ratio of PBH energy density to critical energy density at formation), as: β≲5×10 −19(x φ/6·10 −3) −1(M BH /10 9 g) −1/2( Y φ /10 −14) ; x φ is the fraction of PBH luminosity going into gravitinos or moduli, Y φ is the upper bound imposed by nucleosynthesis on the number density to entropy density ratio of gravitinos or moduli. This notably implies that such PBHs should never come to dominate the cosmic energy density.