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Abstract The possible existence of primordial black holes in the stellar-mass window has received considerable attention because their mergers may contribute to current and future gravitational-wave detections. Primordial black hole mergers, together with mergers of black holes originating from Population III stars, are expected to dominate at high redshifts ( z ≳ 10). However, the primordial black hole merger rate density is expected to rise monotonically with redshift, while Population III mergers can only occur after the birth of the first stars. Next-generation gravitational-wave detectors such as the Cosmic Explorer (CE) and Einstein Telescope (ET) can access this distinctive feature in the merger rates as functions of redshift, allowing for direct measurement of the abundance of the two populations and hence for robust constraints on the abundance of primordial black holes. We simulate four months’ worth of data observed by a CE-ET detector network and perform hierarchical Bayesian analysis to recover the merger rate densities. We find that if the universe has no primordial black holes with masses of  ( 10 M ⊙ ) , the projected upper limit on their abundance f PBH as a fraction of dark matter energy density may be as low as f PBH ∼  ( 10 − 5 ) , about two orders of magnitude lower than the current upper limits in this mass range. If instead f PBH ≳ 10 −4 , future gravitational-wave observations would exclude f PBH = 0 at the 95% credible interval. 

The population properties of intermediate-mass black holes remain largely unknown, and understanding their distribution could provide a missing link in the formation of supermassive black holes and galaxies. Gravitational-wave observations can help fill in the gap from stellar mass black holes to supermassive black holes with masses between ∼100–10⁴M_⊙. In our work, we propose a new method for examining lens populations through lensing statistics of gravitational waves, here focusing on inferring the number density of intermediate-mass black holes through hierarchical Bayesian inference. Simulating ∼200 lensed gravitational-wave signals, we find that existing gravitational-wave observatories at their design sensitivity could either constrain the number density of 10⁶Mpc⁻³within a factor of 10, or place an upper bound of ≲10⁴Mpc⁻³if the true number density is 10³Mpc⁻³. More broadly, our method leaves room for incorporation of additional lens populations, providing a general framework for probing the population properties of lenses in the universe.

 

The population-level distributions of the masses, spins, and redshifts of binary black holes (BBHs) observed using gravitational waves can shed light on how these systems form and evolve. Because of the complex astrophysical processes shaping the inferred BBH population, models allowing for correlations among these parameters will be necessary to fully characterize these sources. We hierarchically analyze the BBH population detected by LIGO and Virgo with a model allowing for correlations between the effective aligned spin and the primary mass and redshift. We find that the width of the effective spin distribution grows with redshift at 98.6% credibility. We determine this trend to be robust under the application of several alternative models and additionally verify that such a correlation is unlikely to be spuriously introduced using a simulated population. We discuss the possibility that this correlation could be due to a change in the natal black hole spin distribution with redshift.

 

The existence of primordial black holes (PBHs), which may form from the collapse of matter overdensities shortly after the Big Bang, is still under debate. Among the potential signatures of PBHs are gravitational waves (GWs) emitted from binary black hole (BBH) mergers at redshiftsz≳ 30, where the formation of astrophysical black holes is unlikely. Future ground-based GW detectors, the Cosmic Explorer and Einstein Telescope, will be able to observe equal-mass BBH mergers with total mass of$\mathit{}(10–100)M_{\odot }$at such distances. In this work, we investigate whether the redshift measurement of a single BBH source can be precise enough to establish its primordial origin. We simulate BBHs of different masses, mass ratios and orbital orientations. We show that for BBHs with total masses between 20M_⊙and 40M_⊙merging atz≥ 40, one can inferz> 30 at up to 97% credibility, with a network of one Einstein Telescope, one 40 km Cosmic Explorer in the US, and one 20 km Cosmic Explorer in Australia. This number reduces to 94% with a smaller network made of one Einstein Telescope and one 40 km Cosmic Explorer in the US. We also analyze how the measurement depends on the Bayesian priors used in the analysis and verify that priors that strongly favor the wrong model yield smaller Bayesian evidences.