We reconsider primordial black hole physics in Randall-Sundrum Type-II universes, focusing on constraints from cosmological and astrophysical observables. We pay particular attention to scenarios that allow the entirety of dark matter to be in the form of higher-dimensional primordial black holes. This is possible for a range of AdS radii and black hole masses. Observable constraints are generally modified due to the changes in the higher-dimensional gravitational sector, and come from low-energy e^± emission, microlensing, and possibly from contributions to unresolved radiation backgrounds. We discuss constraints from the cosmic microwave background due to injection of Hawking quanta into the intergalactic medium. Finally, we comment on recent discussions on the compatibility of higher-dimensional black holes and the KM3-230213A event.

We investigate constraints on the least explored, smallest mass scales of primordial black holes (PBHs), which evaporate prior to Big Bang Nucleosynthesis (BBN). Our study examines the impact of Planck-mass relics on the allowed fraction of dark matter composed of PBHs (f_PBH), as well as on the resulting stochastic gravitational wave background and the formation of primordial binaries. We discuss how these binaries and early mergers lead to longer PBH lifetimes, extending the reach of the stringent BBN constraints to smaller masses than usually expected. We make comprehensive constraint plots on the collapse fraction β and f_PBH (including relics), focusing on ultra-light PBHs.

We make the first calculation of the spectral distortion constraints on the primordial curvature power spectrum in the limit of large cubic non-Gaussianity. This calculation involves computing a 2-loop integral, which we perform analytically. Despite being non-perturbatively non-Gaussian, we show that the constraints only change significantly from the case of Gaussian perturbations in the high-k tail, where spectral distortions become weak. We conclude that generating primordial supermassive black holes requires even more extreme forms of non-Gaussianity. We also argue why the mu-distortion constraint is unlikely to significantly change even in the presence of more extreme local non-Gaussianity.

Phase transitions in the early universe lead to a reduction in the equation of state of the primordial plasma. This exponentially enhances the formation rate of primordial black holes. However, this sensitivity to the equation of state is the same that primordial black hole abundances show to the primordial curvature power spectrum amplitude. In this paper, we investigate peaked power spectra and show the challenges associated with motivating populations of primordial black holes with standard model enhancements. The parametrisation of different power spectra plays an important role in this discussion. The allowed parameter space consistent with a large QCD phase transition impact on the primordial black hole abundance differs greatly. This is particularly evident for broader spectra. We also show that, in our framework, the electroweak phase transition cannot significantly affect the overall abundance.

A well-known route to form primordial black holes in the early universe relies on the existence of unusually large primordial curvature fluctuations, confined to a narrow range of wavelengths that would be too small to be constrained by Cosmic Microwave Background (CMB) anisotropies. This scenario would however boost the generation of μ -type spectral distortions in the CMB due to an enhanced dissipation of acoustic waves. Previous studies of μ -distortion bounds on the primordial spectrum were based on the assumptions of Gaussian primordial fluctuations. In this work, we push the calculation of μ -distortions to one higher order in photon anisotropies. We discuss how to derive bounds on primordial spectrum peaks obeying non-Gaussian statistics under the assumption of local (perturbative or not) non-Gaussianity. We find that, depending on the value of the peak scale, the bounds may either remain stable or get tighter by several orders of magnitude, but only when the departure from Gaussian statistics is very strong. Our results are translated in terms of bounds on primordial supermassive black hole mass in a companion paper.

Primordial black holes (PBHs) can be produced by a range of mechanisms in the early universe. A particular formation channel that connects PBHs with inflationary phenomenology invokes enhanced primordial curvature perturbations at small scales. In this paper, we examine how rapidly the background can transition between different values of the parameters of the Hubble hierarchy in the context of single-clock inflation, which must ultimately derive from a consistent derivative expansion for the background inflaton field. We discuss artefacts associated with instant or very rapid transitions, and consider the impact on the steepest power spectrum growth and the formation of PBHs. In particular, we highlight the robustness of the k 4 steepest growth previously found for single-field inflation with conservatively smoothed transitions and limits on how much the amplitude of the power spectrum can grow, and demonstrate that the PBH mass distribution is sensitive to the artefacts, which go away when the transitions are smoothed. We also show that the mass distribution is relatively insensitive to the steepness of the growth and subsequent decay of the power spectrum, depending primarily on the peak amplitude and the presence of any plateaus that last more than an e-fold. The shape of the power spectrum can of course be constrained by other tracers, and so understanding the physical limitations on its shape remains a pertinent question.

Explaining the origin of supermassive black holes via a primordial origin is severely challenged by the tight spectral distortion constraints on the amplitude of the primordial perturbations. Following the first calculation of how the mu constraints are modified by non-Gaussianity in a companion paper, we here make the first robust constraints on primordial black hole formation under large non-Gaussianity. Even the infinite f NL limit is insufficiently non-Gaussian but much higher-order non-Gaussianity of the form R = R 5 G may allow the formation of any mass primordial black hole without conflicting with distortion constraints. We caution that such extreme models face other challenges.

All single-field inflationary models invoke varying degrees of tuning in order to account for cosmological observations. Mechanisms that generate primordial black holes (PBHs) from enhancement of primordial power at small scales posit inflationary potentials that transiently break scale invariance and possibly adiabaticity over a range of modes. This requires additional tuning on top of that required to account for observations at scales probed by cosmic microwave background (CMB) anisotropies. In this paper we study the parametric dependence of various single-field models of inflation that enhance power at small scales and quantify the degree to which coefficients in the model construction have to be tuned in order for certain observables to lie within specified ranges. We find significant tuning: changing the parameters of the potentials by between one part in a hundred and one part in $10^8$ (depending on the model) is enough to change the power spectrum peak amplitude by an order one factor. The fine-tuning of the PBH abundance is larger still by 1-2 orders of magnitude. We highlight the challenges imposed by this tuning on any given model construction. Furthermore, polynomial potentials appear to require significant additional fine-tuning to also match the CMB observations.

Primordial black holes (PBHs) can be produced by a range of mechanisms in the early universe. A particular formation channel that connects PBHs with inflationary phenomenology invokes enhanced primordial curvature perturbations at small scales. In this paper, we examine how rapidly the background can transition between different values of the parameters of the Hubble hierarchy in the context of single-clock inflation, which must ultimately derive from a consistent derivative expansion for the background inflaton field. We discuss artefacts associated with instant or very rapid transitions, and consider the impact on the steepest power spectrum growth and the formation of PBHs. In particular, we highlight the robustness of the $k^4$ steepest growth previously found for single-field inflation with conservatively smoothed transitions and limits on how much the amplitude of the power spectrum can grow, and demonstrate that the PBH mass distribution is sensitive to the artefacts, which go away when the transitions are smoothed. We also show that the mass distribution is relatively insensitive to the steepness of the growth and subsequent decay of the power spectrum, depending primarily on the peak amplitude and the presence of any plateaus that last more than an e-fold. The shape of the power spectrum can of course be constrained by other tracers, and so understanding the physical limitations on its shape remains a pertinent question.

We examine the shape of the primordial black hole mass distribution arising from a peak in the primordial power spectrum. In light of improvements to the modeling, we revisit the claim that the effects of critical collapse produce a distribution that is not described by the commonly assumed lognormal, showing that this conclusion remains valid, particularly for narrow peaks where the shape of the mass distribution is insensitive to the peak properties and critical collapse determines a minimum width. We propose some alternative models that may better describe the shape, both for the narrow peak case and for much broader peaks where the effect of the peak shape is significant. We highlight the skew-lognormal and a generalized model motivated by the physics of critical collapse as the best of these possible alternatives. These models can be used as an accurate and fast approximation to the numerically calculated mass distribution, allowing for efficient implementation in an MCMC analysis. We advocate the use of one of these two models instead of the lognormal with sufficiently accurate data, such as future LIGO-Virgo observations, or when considering strongly mass dependent constraints on the PBH abundance.

These lecture notes are based on those presented at the Theoretical Aspects of Astroparticle Physics, Cosmology and Gravitation School at the Galileo Galilee Institute in Florence in 2021, https://agenda.infn.it/event/24368/. They aim to provide a pedagogical introduction and basic working knowledge of single-field inflation including the ultra-slow-roll regime, where the perturbations grow exponentially. This rapid growth is connected to the formation of primordial black holes (PBHs), a special dark matter candidate and probe of the initial conditions of the early universe. Although there are many textbooks and introductory texts about inflation, to the best of our knowledge there is no comparable introduction to ultra-slow-roll inflation. Furthermore, given their recent surge in popularity, there are numerous research articles and reviews on primordial black holes, however these notes aim to be more accessible for graduate students and those brand new to the topic. Some problems and solutions to primordial black hole-related calculations are also included. The reader of these lecture notes should come away being able to calculate the present-day abundance of primordial black holes produced from the density fluctuations left over at the end of single-field inflation with an ultra-slow-roll phase, and understand how this abundance compares with current observational constraints.

It is commonly assumed that the energy density of the Universe was dominated by radiation between reheating after inflation and the onset of matter domination 54,000 years later. While the abundance of light elements indicates that the Universe was radiation dominated during Big Bang Nucleosynthesis (BBN), there is scant evidence that the Universe was radiation dominated prior to BBN. It is therefore possible that the cosmological history was more complicated, with deviations from the standard radiation domination during the earliest epochs. Indeed, several interesting proposals regarding various topics such as the generation of dark matter, matter-antimatter asymmetry, gravitational waves, primordial black holes, or microhalos during a nonstandard expansion phase have been recently made. In this paper, we review various possible causes and consequences of deviations from radiation domination in the early Universe - taking place either before or after BBN - and the constraints on them, as they have been discussed in the literature during the recent years.

We consider a disformal coupling between Standard Model matter and a cubic Galileon scalar sector, assumed to be a relict of some other physics that solves the cosmological constant problem rather than a solution in its own right. This allows the energy density carried by the Galileon scalar to be sufficiently small that it evades stringent constraints from the integrated Sachs-Wolfe effect, which otherwise rules out the cubic Galileon theory. Although the model with disformal coupling does not exhibit Vainshtein screening, we show there is a cosmological 'screening-like' phenomenon in which the energy density carried by the Galileon scalar is suppressed during matter domination when the quadratic and cubic Galileon operators are both relevant. We obtain the explicit 3+1 form of Maxwell's equations in the presence of the disformal coupling, and the wave equations that govern electromagnetic waves. The disformal coupling is known to generate a small mass that modifies their velocity of propagation. We use the WKB approximation to study electromagnetic waves in this theory and show that, despite remarkable recent constraints from the LIGO/Virgo observatories that restrict the difference in propagation velocity between electromagnetic and gravitational radiation to roughly 1 part in 10(15), the disformal coupling is too weak to be constrained by events such as GW170817 or by the dispersion of electromagnetic radiation at different wavelengths.

Astroparticle physics is undergoing a profound transformation, due to a series of extraordinary new results, such as the discovery of high-energy cosmic neutrinos with IceCube, the direct detection of gravitational waves with LIGO and Virgo, and many others. This white paper is the result of a collaborative effort that involved hundreds of theoretical astroparticle physicists and cosmologists, under the coordination of the European Consortium for Astroparticle Theory (EuCAPT). Addressed to the whole astroparticle physics community, it explores upcoming theoretical opportunities and challenges for our field of research, with particular emphasis on the possible synergies among different subfields, and the prospects for solving the most fundamental open questions with multi-messenger observations.

We compare primordial black hole (PBH) constraints on the power spectrum and mass distributions using the traditional Press Schechter formalism, peaks theory, and a recently developed version of peaks theory relevant to PBHs. We show that, provided the PBH formation criteria and the power spectrum smoothing are treated consistently, the constraints only vary by ∼ 10% between methods (a difference that will become increasingly important with better data). Our robust constraints from PBHs take into account the effects of critical collapse, the non-linear relation between ζ and δ, and the shift from the PBH mass to the power spectrum peak scale. We show that these constraints are remarkably similar to the pulsar timing array (PTA) constraints impacting the black hole masses detected by LIGO and Virgo, but that the μ-distortion constraints rule out supermassive black hole (SMBH) formation and potentially even the much lighter mass range of ∼(1–100) M☉ that LIGO/Virgo probes.

We examine the shape of the primordial black hole mass distribution arising from a peak in the primordial power spectrum. We show that, for sufficiently narrow peaks, the true mass distribution deviates significantly from lognormal, the most commonly assumed form of the mass distribution. The lognormal approximation is outperformed by a number of similar distributions which can generate negative skewness in log-mass. We highlight the skew-lognormal as the best of these possible modifications and suggest it be used instead of the lognormal with sufficiently accurate data, such as future LIGO-Virgo observations.

We have calculated the detectable merger rate of primordial black holes, as a function of the redshift, as well as the binary's mass ratio, total mass and chirp mass (observables that have not previously been explored in great detail for PBHs). We consider both the current and design sensitivity of LIGO and five different primordial black hole mass functions, as well as showing a comparison to a predicted astrophysical black hole merger rate. We show that the empirical preference for nearly equal-mass binaries in current LIGO/Virgo data can be consistent with a PBH hypothesis once observational selection effects are taken into account. However, current data do exclude some PBH mass distributions, and future data may be able to rule out the possibility that all observed BH mergers had a primordial origin.

We conduct a thorough Bayesian analysis of the possibility that the black hole merger events seen in gravitational waves are primordial black hole (PBH) mergers. Using the latest merger rate models for PBH binaries drawn from a lognormal mass function we compute posterior parameter constraints and Bayesian evidences using data from the first two observing runs of LIGO-Virgo. We account for theoretical uncertainty due to possible disruption of the binary by surrounding PBHs, which can suppress the merger rate significantly. We also consider simple astrophysically motivated models and find that these are favoured decisively over the PBH scenario, quantified by the Bayesian evidence ratio. Paying careful attention to the influence of the parameter priors and the quality of the model fits, we show that the evidence ratios can be understood by comparing the predicted chirp mass distribution to that of the data. We identify the posterior predictive distribution of chirp mass as a vital tool for discriminating between models. A model in which all mergers are PBH binaries is strongly disfavoured compared with astrophysical models, in part due to the over-prediction of heavy systems having $\mathcal{M}_{{\rm chirp}} \gtrsim 40 \, M_\odot$ and positive skewness over the range of observed masses which does not match the observations. We find that the fit is not significantly improved by adding a maximum mass cut-off, a bimodal mass function, or imposing that PBH binaries form at late times. We argue that a successful PBH model must either modify the lognormal shape of the initial mass function significantly or abandon the hypothesis that all observed merging binaries are primordial. We develop and apply techniques for analysing PBH models with gravitational wave data which will be necessary for robust statistical inference as the gravitational wave source sample size increases.

If the primordial curvature perturbation followed a Gaussian distribution, primordial black holes (PBHs) will be Poisson distributed with no additional clustering. We consider local non-Gaussianity and its impact on the initial PBH clustering and mass function due to mode coupling between long and short wavelength modes. We show that even a small amount of non-Gaussianity results in a significant enhancement on the PBH initial clustering and subsequent merger rate and that the PBH mass function shifts to higher mass PBHs. However, as the clustering becomes strong, the local number density of PBHs becomes large, leading to a large theoretical uncertainty in the merger rate.

The expansion of the Universe is understood to have accelerated during two epochs: in its very first moments during a period of Inflation and much more recently, at $z < 1$, when Dark Energy is hypothesized to drive cosmic acceleration. The undiscovered mechanisms behind these two epochs represent some of the most important open problems in fundamental physics. The large cosmological volume at $2 < z < 5$, together with the ability to efficiently target high-$z$ galaxies with known techniques, enables large gains in the study of Inflation and Dark Energy. A future spectroscopic survey can test the Gaussianity of the initial conditions up to a factor of ~50 better than our current bounds, crossing the crucial theoretical threshold of $\sigma(f_{NL}^{\rm local})$ of order unity that separates single field and multi-field models. Simultaneously, it can measure the fraction of Dark Energy at the percent level up to $z = 5$, thus serving as an unprecedented test of the standard model and opening up a tremendous discovery space.