The primordial black hole (PBH) abundance evaluated by the conventional Press-Schechter (PS) probability distribution is shown to be equivalent to the high-peak limit of a special point-like peak statistics via unphysical dimensionality reduction of the Bardeen-Bond-Kaiser-Szalay (BBKS) theory. The fact that PBHs are formed at high peak values $ν_c \gg 1$ leads to a systematic bias proportional to $ν_c^3$ between the predictions of the PS method and the physical BBKS peak theory in a general three-dimensional spatial configuration. As long as realistic PBHs are collapsed from three-dimensional density peaks in space, the systematic bias led by $ν_c^3$ implies a significant underestimation of the PBH abundance reported by the PS method. For the inflationary spectrum in the narrow-spike class, the underestimation in the extended mass functions is further enlarged by at least a factor of $10^{2.5}$ in all mass range, indicating a severer constraint to models in the favor of considering PBHs as all dark matter in a certain mass range.
It has been suggested that superheavy charged particles might have been born in primordial bound pairs at the end of cosmic inflation. Such pairs have been proposed as a source of ultra-high energy cosmic rays (UHECR). We show that primordial bound pairs of magnetic monopoles larger than $10^{-9}$ cm quickly thermolise due to the interaction with primordial electron-positron plasma and any such initial primordial concentration is washed out. The final concentration will therefore be defined by their equilibrium abundance.
In the model where Primordial Black Holes (PBHs) form from large primordial curvature (C) perturbations, i.e., CPBHs, constraints on PBH abundance provide in principle constraints on the primordial curvature power spectrum. This connection however depends necessarily on the details of PBH formation mechanism. In this paper we provide, for the first time, constraints on the primordial curvature power spectrum from the latest limits on PBH abundance, taking into account all the steps from gravitational collapse in real space to PBH formation. In particular, we use results from numerical relativi…
We carried out an exploratory analysis of the contribution of the underlying stellar absorption to the total uncertainty of the abundance of primordial helium using simple stellar populations models and observational data from the Sloan Digital Sky Survey. Results indicate that our analysis yields a lower limit to the error on the helium abundance determination if the stellar absorption is neglected.
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…
We investigate features of Gravitational Waves (GWs) induced by primordial density fluctuations with a large amplitude peak associated with formation of Primordial Black Holes (PBHs). It is shown that the spectrum of induced GW is insensitive to the width of the peak in wavenumber space provided it is below a certain value, but the amplitude of the spectrum reduces at the peak frequency and decreases faster at low frequencies for a larger width. A correspondence between the GW amplitude and PBH abundance is also investigated incorporating the peak width. We find that PBHs with masses 10^{20-26…
The evolution with time of the abundance of galaxy clusters is very sensitive to the statistical properties of the primordial density perturbations. It can thus be used to probe small deviations from Gaussianity in the initial conditions. The characterization of such deviations would help distinguish between different inflationary scenarios, and provide us with information on physical processes which took place in the early Universe. We have found that when the information contained in the galaxy cluster counts is used to reconstruct the dark energy equation of state as a function of redshift,…
If primordial black holes (PBHs) seeded the supermassive black holes (SMBHs) at the centers of high-redshift quasars, then the gas surrounding these black holes may reveal nucleosynthetic clues to their primordial origins. We present predictions of altered primordial abundances around PBHs massive enough to seed SMBHs at z~6-7.5. We find that if PBHs with initial masses of ~10^5 M$_{\odot}$ are responsible for such SMBHs, they may produce primordial Deuterium and Helium fractions enhanced by >~ 10%, and Lithium abundance depleted by >~10%, at distances of up to ~ a comoving kiloparsec away fro…
Observations of metal-poor extragalactic H II regions allow the determination of the primordial helium abundance, Y_p. The He I emissivities are the foundation of the model of the H II region's emission. Porter, Ferland, Storey, & Detisch (2012) have recently published updated He I emissivities based on improved photoionization cross-sections. We incorporate these new atomic data and update our recent Markov Chain Monte Carlo analysis of the dataset published by Izotov, Thuan, & Stasinska (2007). As before, cuts are made to promote quality and reliability, and only solutions which fit the data…
Primordial black holes represent a unique probe to constrain the early universe on small scales - providing the only constraints on the primordial power spectrum on the majority of scales. However, these constraints are strongly dependent on even small amounts of non-Gaussianity, which is unconstrained on scales significantly smaller than those visible in the CMB. This paper goes beyond previous considerations to consider the effects of a bispectrum of the equilateral, orthogonal and local shapes with arbitrary magnitude upon the abundance of primordial black holes. Non-Gaussian density maps o…
The non-singular bouncing cosmology is an alternative paradigm to inflation, wherein the background energy density vanishes at the bounce point, in the context of Einstein gravity. Therefore, the non-linear effects in the evolution of density fluctuations ($δρ$) may be strong in the bounce phase, which potentially provides a mechanism to enhance the abundance of primordial black holes (PBHs). This article presents a comprehensive illustration for PBH enhancement due to the bounce phase. To calculate the non-linear evolution of $δρ$, the Raychaudhuri equation is numerically solved here. Since t…
The formation and abundance of primordial black holes (PBHs) arising from the curvature perturbation $ζ$ is studied. The non-linear relation between $ζ$ and the density contrast $δ$ means that, even when $ζ$ has an exactly Gaussian distribution, significant non-Gaussianities affecting PBH formation must be considered. Numerical simulations are used to investigate the critical value and the mass of PBHs which form, and peaks theory is used to calculate the mass fraction of the universe collapsing to form PBHs at the time of formation. A formalism to calculate the total present day PBH abundance…
Primordial or big bang nucleosynthesis (BBN) is one of the three historical strong evidences for the big bang model. The recent results by the Planck satellite mission have slightly changed the estimate of the baryonic density compared to the previous WMAP analysis. This article updates the BBN predictions for the light elements using the cosmological parameters determined by Planck, as well as an improvement of the nuclear network and new spectroscopic observations. There is a slight lowering of the primordial Li/H abundance, however, this lithium value still remains typically 3 times larger …
The light relic density affects the thermal and expansion history of the early Universe leaving a number of observable imprints. We focus on the primordial abundances of light elements produced during the process of Big Bang nucleosynthesis which are influenced by the light relic density. Primordial abundances can be used to infer the density of light relics and thereby serve as a probe of physics beyond the Standard Model. We calculate the observational uncertainty on primordial light element abundances and associated quantities that would be required in order for these measurements to achiev…
Assuming the best numerical value for the cosmic baryonic density and the existence of three neutrino flavors, standard big bang nucleosynthesis is a parameter-free model. It is important to assess if the observed primordial abundances can be reproduced by simulations. Numerous studies have shown that the simulations overpredict the primordial $^7$Li abundance by a factor of $\approx$ $3$ compared to the observations. The discrepancy may be caused by unknown systematics in $^7$Li observations, poorly understood depletion of lithium in stars, errors in thermonuclear rates that take part in the …
We generalize Doroshkevich's celebrated formulae for the eigenvalues of the initial shear field associated with Gaussian statistics to the local non-Gaussian f_{nl} model. This is possible because, to at least second order in f_{nl}, distributions at fixed overdensity are unchanged from the case f_{nl}=0. We use this generalization to estimate the effect of f_{nl}\ne 0 on the abundance of virialized halos. Halo abundances are expected to be related to the probability that a certain quantity in the initial fluctuation field exceeds a threshold value, and we study two choices for this variable: …
Large-amplitude density perturbations may have collapsed during the radiation dominated epoch of the Universe to form primordial black holes (PBHs). There are several constraints to the abundance of PBHs that stem from evaporation or gravitational effects. Due to the connection between primordial perturbations and the formation of PBHs, constraints on the present-day abundance of PBHs can be translated into limits on the primordial curvature power spectrum. We introduce several new observational and forecasted constraints to the amplitude of the primordial power spectrum and incorporate in our…
The precision measurement of the primordial helium abundance $Y_p$ is a powerful probe of the early Universe. The most common way to determine $Y_p$ is analyses of observations of metal-poor \HII regions found in blue compact dwarf galaxies. We present the spectroscopic sample of 100 \HII regions collected from the Sloan Digital Sky Survey. The final analysed sample consists of our sample and HeBCD database from Izotov et al. 2007. We use a self-consistent procedure to determine physical conditions, current helium abundances, and metallicities of the \HII regions. From a regression to zero met…
The next generation of gravitational-wave experiments, such as Einstein Telescope, Cosmic Explorer and LISA, will test the primordial black hole scenario. We provide a forecast for the minimum testable value of the abundance of primordial black holes as a function of their masses for both the unclustered and clustered spatial distributions at formation. In particular, we show that these instruments may test abundances, relative to the dark matter, as low as $10^{-10}$.
Primordial magnetic field (PMF) is one of the feasible candidates to explain observed large-scale magnetic fields, for example, intergalactic magnetic fields. We present a new mechanism that brings us information about PMFs on small scales based on the abundance of primordial black holes (PBHs). The anisotropic stress of the PMFs can act as a source of the super-horizon curvature perturbation in the early universe. If the amplitude of PMFs is sufficiently large, the resultant density perturbation also has a large amplitude, and thereby, the PBH abundance is enhanced. Since the anisotropic stre…
We present a review on the determination of the primordial helium abundance Yp, based on the study of hydrogen and helium recombination lines in extragalactic HII regions. We also discuss the observational determinations of the increase of helium to the increase of oxygen by mass Delta Y / Delta O, and compare them with predictions based on models of galactic chemical evolution.
The light elements up to 7Li were produced by the Standard Big Bang nucleosynthesis (SBBN) in the early universe assuming standard conditions. All observed primordial abundances of these light elements match very well the predicted ones by this SBBN except for 7Li which seems to be overproduced. It is rather challenging to resolve this discrepancy owing to the diverse possibilities affecting the abundance of lithium. In the present work we focus on non-standard possible solutions such as variation of chemical potential and the neutrino temperatures. In addition, the effect of dark matter is al…
It was proposed that the massive compact halo objects (MCHOs) would be produced during an earlier epoch of cosmology if the density perturbations are between $3 \times 10^{-4}$ and 0.3. Then these objects can accrete dark matter particles onto them due to their high density. If the dark matter is in the form of the weakly interacting massive particles, the MCHOs can have a significant effect on the evolution of cosmology due to the dark matter annihilation within them. Using the WMAP-7 years data, we investigated the constraints on the current abundance of MCHOs ($f_{MCHOs}$) formed during the…
We include the coupling of a heavy sterile neutrino with active neutrinos in the calculation of primordial abundances of light-nuclei. We calculate neutrino distribution functions and primordial abundances, as functions depending on a renormalization of the sterile neutrino distribution function $(a)$, the sterile neutrino mass $(m_s)$ and the mixing angle $(ϕ)$. Using the observable data, we set constrains on these parameters, which have the values $a < 0.60$, $\sin^2 ϕ=0.15$ and $m_s \approx 4$ keV, for a fixed value of the baryon to photon ratio. When the baryon to photon ratio is allowed t…
Abundances of light nuclei formed during primordial nucleosynthesis are predicted by Standard Big Bang Model. The latest data from WMAP, with precision's higher than ever before, provides a motivation to determine theoretical higher order corrections to change in helium abundance and the related parameters. Here we evaluate the QED corrections to the change in these parameters during primordial nucleosynthesis using finite temperature effects at the two loop level. Relative variations in neutron decay rate, total energy density of the universe, relative change in neutrino temperature etc., wit…
The abundance of primordial black holes is currently significantly constrained in a wide range of masses. The weakest limits are established for the small mass objects, where the small intensity of the associated physical phenomenon provides a challenge for current experiments. We used gamma- ray bursts with known redshifts detected by the Fermi Gamma-ray Burst Monitor (GBM) to search for the femtolensing effects caused by compact objects. The lack of femtolensing detection in the GBM data provides new evidence that primordial black holes in the mass range 5 \times 10^{17} - 10^{20} g do not c…
It has been recently established that, if the nonlinear relationship between the overdensity perturbations and the curvature perturbations are taken into account, non-Gaussianity is introduced in the overdensity statistics which alters the expected primordial black hole abundance. This is explored by using the nonlinear relationship between the overdensities and curvature perturbations up to second order where a negative skewness and positive kurtosis aims at lowering and increasing the abundance while an abundance comparable to Gaussian perturbations is obtained by adjusting the amplitude of …
In this paper, the formation of primordial black holes (PBHs) is reinvestigated using inflationary $α$-attractors. Instead of using the conventional Press-Schechter theory to compute the abundance, the optimized peaks theory is used, which was developed in Ref. \cite{Yoo:2018kvb,Yoo:2020dkz}. This method takes into account how curvature perturbations play a rôle in modifying the mass of primordial black holes. Analyzing the model proposed in \cite{Mahbub:2019uhl} it is seen that the horizon mass of the collapsed Hubble patch is larger by $\mathcal{O}(10)$ compared to the usual computation. Mor…
A new upper limit on the amplitude of primordial magnetic field (PMF) is derived by a comparison between a calculation of elemental abundances in big bang nucleosynthesis (BBN) model and the latest observational constraints on the abundances. Updated nuclear reaction rates are adopted in the calculation. Effects of PMF on the abundances are consistently taken into account in the numerical calculation with the precise formulation of changes in physical variables. We find that abundances of 3He and 6Li increase while that of 7Li decreases when the PMF amplitude increases, in the case of the bary…
Primordial molecules were formed during the Dark Ages, i.e. the time between recombination and reionization in the early Universe. The purpose of this article is to analyze the formation of primordial molecules based on heavy elements during the Dark Ages, with elemental abundances taken from different nucleosynthesis models. We present calculations of the full non-linear equation set governing the primordial chemistry. We consider the evolution of 45 chemical species and use an implicit multistep method of variable order of precision with an adaptive stepsize control. We find that the most ab…
Spectroscopic observations of the chemical abundances in metal-poor H II regions provide an independent method for estimating the primordial helium abundance. H II regions are described by several physical parameters such as electron density, electron temperature, and reddening, in addition to y, the ratio of helium to hydrogen. It had been customary to estimate or determine self-consistently these parameters to calculate y. Frequentist analyses of the parameter space have been shown to be successful in these determinations, and Markov Chain Monte Carlo (MCMC) techniques have proven to be very…
The non-observation of Hawking radiation from primordial black holes of $10^{16}$g sets a conservative strong bound on their cosmological abundance. We revisit this bound and show how it can be improved (both in mass reach and strength) by an adequate modeling of the combined AGN and blazar emission in the MeV range. We also estimate the sensitivity to the primordial black hole abundance of a future X-ray experiment capable of identifying a significantly larger number of astrophysical sources contributing to the diffuse background in this energy range.
Based on observations of HII regions and the new computations of the recombination coefficients of the He I lines by Porter et al. (2013) we obtain a primordial helium abundance by mass of $Y_P = 0.2446\pm0.0029$. We consider thirteen sources of error for the $Y_P$ determination, some of them are mainly due to systematic effects, while the rest are mainly due to statistical effects. We compare our results with other determinations of $Y_P$ present in the literature. Combining our $Y_P$ value with computations of primordial nucleosynthesis we find a number of neutrino species $N_{eff} = 2.90\pm…
To place meaningful constraints on Big Bang Nucleosynthesis models, the primordial helium abundance determination is crucial. Low-metallicity HII regions have been used to estimate it since their statistical uncertainties are relatively small. We present a new determination of the primordial helium abundance, based on long slit spectra of the HII region NGC 346 in the small Magellanic cloud. We obtained spectra using three $409'' \times 0.51''$ slits divided in 97 subsets. They cover the range $λ\lambda3600-7400$ of the electromagnetic spectrum. We used PyNeb and standard reduction procedures …
Almost every helium atom in the Universe was created just a few minutes after the Big Bang through a process commonly referred to as Big Bang Nucleosynthesis. The amount of helium that was made during Big Bang Nucleosynthesis is determined by the combination of particle physics and cosmology. The current leading measures of the primordial helium abundance (Y_P) are based on the relative strengths of H I and He I emission lines emanating from star-forming regions in local metal-poor galaxies. As the statistical errors on these measurements improve, it is essential to test for systematics by dev…
Models in which dark matter consists entirely of primordial black holes (PBHs) with masses around $10^{17}$ g are currently unconstrained. However, if PBHs are a component of the Galactic dark matter density, they will inject a large flux of energetic particles into the Galaxy as they radiate. Positrons produced by these black holes will subsequently propagate throughout the Galaxy and annihilate, contributing to the Galactic 511 keV line. Using measurements of this line by the INTEGRAL satellite as a constraint on PBH positron injection, we place new limits on PBH abundance in the mass range …
Advanced LIGO's discovery of gravitational-wave events is stimulating extensive studies on the origin of binary black holes. Assuming that the gravitational-wave events can be explained by binary primordial black hole mergers, we utilize the upper limits on the stochastic gravitational-wave background given by Advanced LIGO as a new observational window to independently constrain the abundance of primordial black holes in dark matter. We show that Advanced LIGO's first observation run gives the best constraint on the primordial black hole abundance in the mass range $1 M_\odot \lesssim M_\text…
Muon abundance is required for the understanding of several fundamental questions regarding properties of the primordial Universe. In this paper we evaluate the production and decay rates of muons in the cosmic plasma as a function of temperature. This allows us to determine when exactly the muon abundance disappears. When the Universe cools below the temperature $kT_\mathrm{disappear}\approx 4.135$ MeV the muon decay rate overwhelms production rates and muons vanish quasi-instantaneously from the Universe. Interestingly, we show that at $T_\mathrm{disappear}$ the muon number is nearly equal t…
The formation of Primordial Black Holes (PBHs) through the collapse of large fluctuations in the early universe is a rare event. This manifests itself, for instance, through the non-Gaussian tail of the formation probability. To compute such probability and the abundance of PBHs, the curvature perturbation is frequently adopted. In this note we emphasize that its use does not provide the correct PBH formation probability. Through a path-integral approach we show that the exact calculation of the PBH abundance demands the knowledge of multivariate joint probabilities of the curvature perturbati…
The idea that dark matter can be made of intermediate-mass primordial black holes in the $10M_\odot \lesssim M \lesssim 200M_\odot$ range has recently been reconsidered, particularly in the light of the detection of gravitational waves by the LIGO experiment. The existence of even a small fraction of dark matter in black holes should nevertheless result in noticeable quasar gravitational microlensing. Quasar microlensing is sensitive to any type of compact objects in the lens galaxy, to their abundance, and to their mass. We have analyzed optical and X-ray microlensing data from 24 gravitation…
We compute the primordial mirror helium He' mass fraction emerging from Big Bang nucleosynthesis in the mirror sector of particles in the presence of kinetic mixing between photons and mirror photons. We explore the kinetic mixing parameter (epsilon) values relevant for cosmology and which are also currently probed by the dark matter direct detection experiments. In particular, we find that for epsilon \sim 10^{-9}, as suggested by the DAMA/Libra and other experiments, a large He' mass fraction (Y_{He'} \approx 90%) is produced. Such a large value of the primordial He' mass fraction will have …
A significant abundance of primordial black hole (PBH) dark matter can be produced by curvature perturbations with power spectrum $Δ_ζ^2(k_{\mathrm{peak}})\sim \mathcal{O}(10^{-2})$ at small scales, associated with the generation of observable scalar induced gravitational waves (SIGWs). However, the primordial non-Gaussianity may play a non-negligible role, which is not usually considered. We propose two inflation models that predict double peaks of order $\mathcal{O}(10^{-2})$ in the power spectrum and study the effects of primordial non-Gaussianity on PBHs and SIGWs. This model is driven by …
We study the formation of primordial black holes when they are generated by the collapse of large overdensities in the early universe. Since the density contrast is related to the comoving curvature perturbation by a nonlinear relation, the overdensity statistics is unavoidably non-Gaussian. We show that the abundance of primordial black holes at formation may not be captured by a perturbative approach which retains the first few cumulants of the non-Gaussian probability distribution. We provide two techniques to calculate the non-Gaussian abundance of primordial black holes at formation, one …
We consider the application of peaks theory to the calculation of the number density of peaks relevant for primordial black hole (PBH) formation. For PBHs, the final mass is related to the amplitude and scale of the perturbation from which it forms, where the scale is defined as the scale at which the compaction function peaks. We therefore extend peaks theory to calculate not only the abundance of peaks of a given amplitude, but peaks of a given amplitude and scale. A simple fitting formula is given in the high-peak limit relevant for PBH formation. We also adapt the calculation to use a Gaus…
We study the predictions of anomalous inflationary models on the abundance of structures in large scale structure observations. The anomalous features encoded in primordial curvature perturbation power spectrum are (a): localized feature in momentum space, (b): hemispherical asymmetry and (c): statistical anisotropies. We present a model-independent expression relating the number density of structures to the changes in the matter density variance. Models with localized feature can alleviate the tension between observations and numerical simulations of cold dark matter structures on galactic sc…
The dissipation effects of primordial magnetic fields on the primordial elemental abundances were investigated. When a magnetic field reconnects, its energy is converted to the kinetic energy of charged particles, as observed for solar energetic particles arriving on earth. This accelerates the cosmic background nuclei, and energetic nuclei induce nonthermal reactions. A constraint on the dissipation is derived from a theoretical calculation of the nonthermal reactions during Big Bang nucleosynthesis. We found that observations of the Li and D abundances can be explained if 0.01--0.1 % of the …
Observational measures of the primordial helium mass fraction, $Y_{\rm P}$, are of interest for cosmology and fundamental particle physics. Current measures obtained from H II regions agree with the Standard Model prediction to approximately 1% precision, although these determinations may be affected by systematic uncertainties. This possibility can only be tested by independently measuring the helium abundance in new ways. Here, we propose a novel method to obtain a measurement of $Y_{\rm P}$ using hydrogen and helium recombination line emission from RELHICs: pristine, gas-rich but star-free …
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…
