Unstable domain wall (DW) networks in the early universe are cosmologically viable and can emit a large amount of gravitational waves (GW) before annihilating. As such, they provide an interpretation for the recent signal reported by Pulsar Timing Array (PTA) collaborations. A related important question is whether such a scenario also leads to significant production of Primordial Black Holes (PBH). We investigate both GW and PBH production using 3D numerical simulations in an expanding background, with box sizes up to $N=3240$, including the annihilation phase. We find that: i) the network decays exponentially, i.e. the false vacuum volume drops as $\sim \exp(-η^3)$, with $η$ the conformal time; ii) the GW spectrum is larger than traditional estimates by more than one order of magnitude, due to a delay between DW annihilation and the sourcing of GWs. We then present a novel semi-analytical method to estimate the PBH abundances: rare false vacuum pockets of super-Hubble size collapse to PBHs if their energy density becomes comparable to the background when they cross the Hubble scale. Smaller (but more abundant) pockets will instead collapse only if they are close to spherical. This introduces very large uncertainties in the final PBH abundance. The first phenomenological implication is that the DW interpretation of the PTA signal is compatible with observational constraints on PBHs, within the uncertainties. Second, in a different parameter region, the dark matter can be entirely in the form of asteroid-mass PBHs from the DW collapse. Remarkably, this would also lead to a GW background in the observable range of LIGO-Virgo-KAGRA and future interferometers, such as LISA and Einstein Telescope.
The angular momentum (spin) acquisition by a collapsing domain wall at the cosmological radiation-dominated stage is investigated. During the collapses, primordial black holes and their clusters can be born in various mass ranges. Spin accumulation occurs under the influence of tidal gravitational perturbations from the surrounding density inhomogeneities at the epoch when the domain wall crosses the cosmological horizon. It is shown that the dimensionless spin parameter can have the small values $a_S<1$ only for primordial black holes with masses $M>10^{-3}M_\odot$, whereas less massive black…
We investigate the capability of pulsar timing arrays (PTAs) as a probe of primordial black holes (PBHs), which might constitute the Galactic dark matter. A PBH passing nearby the Earth or a pulsar gives an impulse acceleration and induces residuals on otherwise orderly pulsar timing data. We show that the timing residuals induced at pulsars are optimal for searching heavier PBHs than those at the Earth, and the two probes are highly complemental. Future facilities like SKA could detect PBHs with masses around 10^(22-28) g even if only a small fraction (< 1%) of the Galactic dark matter consis…
The gravitational waves measured at LIGO are presumed here to come from merging primordial black holes. We ask how these primordial black holes could arise through inflationary models while not conflicting with current experiments. Among the approaches that work, we investigate the opportunity for corroboration through experimental probes of gravitational waves at pulsar timing arrays. We provide examples of theories that are already ruled out, theories that will soon be probed, and theories that will not be tested in the foreseeable future. The models that are most strongly constrained are th…
Pulsars act as accurate clocks, sensitive to gravitational redshift and acceleration induced by transiting clumps of matter. We study the sensitivity of pulsar timing arrays (PTAs) to single transiting compact objects, focusing on primordial black holes and compact subhalos in the mass range from $10^{-12} M _{\odot}$ to well above $100~M_\odot$. We find that the Square Kilometer Array can constrain such objects to be a subdominant component of the dark matter over this entire mass range, with sensitivity to a dark matter sub-component reaching the sub-percent level over significant parts of t…
The recent discovery of gravitational waves from merging black holes has generated interest in primordial black holes as a possible component of the dark matter. In this paper, we show that pulsar timing may soon have sufficient data to constrain $1$-$1000\,M_{\odot}$ primordial black holes via the non-detection of a third-order Shapiro time delay as the black holes move around the Galactic halo. We present the results of a Monte Carlo simulation which suggests that future data from known pulsars may be capable of constraining the PBH density more stringently than other existing methods in the…
Implications of Pulsar Timing Array Data for Scalar-Induced Gravitational Waves and Primordial Black Holes: Primordial Non-Gaussianity $f_{\mathrm{NL}}$ Considered
In this paper, we explore the possibility of accreting primordial black holes as the source of heating for the collapsing gas in the context of the direct collapse black hole scenario for the formation of super-massive black holes (SMBHs) at high redshifts, $z\sim 6-7$. One of the essential requirements for the direct collapse model to work is to maintain the temperature of the in falling gas at $\approx 10^4$ K. We show that even under the existing abundance limits, the primordial black holes of masses $\gtrsim 10^{-2} \ {\rm M}_\odot$, can heat the collapsing gas to an extent that the ${\rm …
We study the spin of primordial black holes produced by the collapse of large inhomogeneities in the early universe. Since such primordial black holes originate from peaks, that is, from maxima of the local overdensity, we resort to peak theory to obtain the probability distribution of the spin at formation. We show that the spin is a first-order effect in perturbation theory: it results from the action of first-order tidal gravitational fields generating first-order torques upon horizon-crossing, and from the asphericity of the collapsing object. Assuming an ellipsoidal shape, the typical val…
Primordial black holes (PBHs) are one of the candidates to explain the gravitational wave (GW) signals observed by the LIGO detectors. Among several phenomena in the early Universe, cosmic inflation is a major example to generate PBHs from large primordial density perturbations. In this paper, we discuss the possibility to interpret the observed GW events as mergers of PBHs which are produced by cosmic inflation. The primordial curvature perturbation should be large enough to produce a sizable amount of PBHs and thus we have several other probes to test this scenario. We point out that the cur…
The NANOGrav, Parkes, European, and International Pulsar Timing Array (PTA) Collaborations have reported evidence for a common-spectrum process that can potentially correspond to a stochastic gravitational wave background (SGWB) in the 1--100 nHz frequency range. We consider the scenario in which this signal is produced by magnetohydrodynamic (MHD) turbulence in the early Universe, induced by a nonhelical primordial magnetic field at the energy scale corresponding to the quark confinement phase transition. We perform MHD simulations to study the dynamical evolution of the magnetic field and co…
Ultracompact Minihalos (UCMHs) have been proposed as a type of dark matter sub-structure seeded by large-amplitude primordial perturbations and topological defects. UCMHs are expected to survive to the present era, allowing constraints to be placed on their cosmic abundance using observations within our own Galaxy. Constraints on their number density can be linked to conditions in the early universe that impact structure formation, such as increased primordial power on small scales, generic weak non-Gaussianity, and the presence of cosmic strings. We use new constraints on the abundance of UCM…
Probing Primordial Black Hole Mergers in Clusters with Pulsar Timing Data
a Service de Physique Th\'eorique, Brussels Laboratory of the Universe BLU-ULB, Universit\'e Libre de Bruxelles, Boulevard du Triomphe, CP225, 1050 Brussels, Belgium
It has been proposed that primordial gas in early dark matter halos, with virial temperatures above 10^4 K, can avoid fragmentation and undergo rapid collapse, possibly resulting in a supermassive black hole (SMBH). This requires the gas to avoid cooling and to remain at temperatures near T=10^4 K. We show that this condition can be satisfied in the presence of a sufficiently strong primordial magnetic field, which heats the collapsing gas via ambipolar diffusion. If the field has a strength above B = 3.6 (comoving) nG, the collapsing gas is kept warm (T=10^4K) until it reaches the critical de…
We argue that the global signal of neutral hydrogen 21cm line can be a powerful probe of primordial power spectrum on small scales. Since the amplitude of small scale primordial fluctuations is important to determine the early structure formation and the timing when the sources of Lyman $α$ photons are produced, they in turn affect the neutral hydrogen 21cm line signal. We show that the information of the position of the absorption trough can severely constrain the small scale amplitude of primordial fluctuations once astrophysical parameters relevant to the 21cm line signal are fixed. We also…
In this paper, the criterion used to determine whether a density perturbation will collapse to form a primordial black hole (PBH) is re-examined, in respect of its use to determine the abundance of PBHs. There is particular focus on which parameter to use, the time at which the abundance should be calculated, and the use of different smoothing functions. It is concluded that, with the tools currently available, the smoothed density contrast should be used rather than the peak value, and should be calculated from the time-independent component of the density contrast in the super-horizon limit …
Primordial black hole (PBH) mergers have been proposed as an explanation for the gravitational wave events detected by the LIGO collaboration. Such PBHs may be formed in the early Universe as a result of the collapse of extremely rare high-sigma peaks of primordial fluctuations on small scales, as long as the amplitude of primordial perturbations on small scales is enhanced significantly relative to the amplitude of perturbations observed on large scales. One consequence of these small-scale perturbations is generation of stochastic gravitational waves that arise at second order in scalar pert…
The NANOGrav collaboration for the pulsar timing array (PTA) observation recently announced evidence of an isotropic stochastic process, which may be the first detection of the stochastic gravitational-wave (GW) background. We discuss the possibility that the signal is caused by the second-order GWs associated with the formation of solar-mass primordial black holes (PBHs). This possibility can be tested by future interferometer-type GW observations targeting the stochastic GWs from merger events of solar-mass PBHs as well as by updates of PTA observations.
If the black holes detected by LIGO/VIRGO are primordial black holes (PBHs) sourcing from a large primordial curvature perturbation on small scales, the corresponding induced gravitational waves (GWs) would peak at nanohertz that is detectable by the current and future observations of pulsar timing array (PTA). In this paper we show that with the mass function estimated from the merger rate of LIGO O1 and O2 events, the induced GWs from such a curvature perturbation with a Gaussian narrow peak at some small scale would be in a seemingly mild tension with current constraints from PTA. However, …
We present a scenario that ameliorates the tuning problems present in models of primordial black hole dark matter from inflation. Our setup employs the advantages of gravitational collapse in a long epoch of early matter domination with reheating temperature $\lesssim 10^{6}~\text{GeV}$. Furthermore, we make use of a string-inspired class of models where the inflaton is identified with a non-compact axion field. In this framework, the presence of multiple local minima in the inflaton potential can be traced back to an approximate discrete shift symmetry. This scenario allows the formation of p…
We study the effects of velocity dispersion on the formation of primordial black holes~(PBHs) in a matter-dominated era. The velocity dispersion is generated through the nonlinear growth of perturbations and has the potential to impede the gravitational collapse and thereby the formation of PBHs. To make discussions clear, we consider two distinct length scales. The larger one is where gravitational collapse occurs which could lead to PBH formation, and the smaller one is where the velocity dispersion develops due to nonlinear interactions. We estimate the effect of the velocity dispersion on …
We propose and study the new (generalized) E-type $α$-attractor models of inflation, in order to include formation of primordial black holes (PBHs). The inflaton potential has a near-inflection point where slow-roll conditions are violated, thus leading to large scalar perturbations collapsing to PBHs later. An ultra-slow roll (short) phase exists between two (longer) phases of slow-roll inflation. We numerically investigate the phases of inflation, derive the power spectrum of scalar perturbations and calculate the PBHs masses. For certain values of the parameters, the asteroid-size PBHs can …
The diffuse backgrounds of relic gravitons with frequencies ranging between the aHz band and the GHz region encode the ultimate information on the primeval evolution of the plasma and on the underlying theory of gravity well before the electroweak epoch. While the temperature and polarization anisotropies of the microwave background radiation probe the low-frequency tail of the graviton spectra, during the next score year the pulsar timing arrays and the wide-band interferometers (both terrestrial and hopefully space-borne) will explore a much larger frequency window encompassing the nHz domai…
Angular momentum plays very important roles in the formation of PBHs in the matter-dominated phase if it lasts sufficiently long. In fact, most collapsing masses are bounced back due to centrifugal force, since angular momentum significantly grows before collapse. As a consequence, most of the formed PBHs are rapidly rotating near the extreme value $a_{*}=1$, where $a_{*}$ is the nondimensional Kerr parameter at their formation. The smaller the density fluctuation $σ_{H}$ at horizon entry is, the stronger the tendency towards the extreme rotation. Combining the effect of angular momentum with …
