Gravitational Waves from Primordial Black Hole Mergers (1707.01480v3)

Abstract: We study the production of primordial black hole (PBH) binaries and the resulting merger rate, accounting for an extended PBH mass function and the possibility of a clustered spatial distribution. Under the hypothesis that the gravitational wave events observed by LIGO were caused by PBH mergers, we show that it is possible to satisfy all present constraints on the PBH abundance, and find the viable parameter range for the lognormal PBH mass function. The non-observation of gravitational wave background allows us to derive constraints on the fraction of dark matter in PBHs, which are stronger than any other current constraint in the PBH mass range $0.5-30M_\odot$. We show that the predicted gravitational wave background can be observed by the coming runs of LIGO, and non-observation would indicate that the observed events are not of primordial origin. As the PBH mergers convert matter into radiation, they may have interesting cosmological implications, for example, in the context of relieving the tension between the high and low redshift measurements of the Hubble constant. However, we find that these effects are negligible as, after recombination, no more that $1\%$ of DM can be converted into gravitational waves.

• The paper demonstrates that an extended lognormal PBH mass function reconciles LIGO merger rates with dark matter constraints.
• It employs models of early universe binary formation and late-universe gravitational capture to assess PBH merger mechanisms.
• Results predict an observable stochastic gravitational wave background, offering a testable signature for the primordial origin hypothesis.

Gravitational Waves from Primordial Black Hole Mergers: An Analysis

The paper "Gravitational Waves from Primordial Black Hole Mergers" by Raidal, Vaskonen, and Veermäe presents an in-depth exploration of the possibility that the gravitational wave (GW) events detected by LIGO originate from mergers of primordial black holes (PBHs). The authors integrate extended mass functions and potential clustering effects of the PBHs to paper the rates and cosmological implications of these mergers.

PBHs have been hypothesized since the early 1970s, and their formation is linked to high-density fluctuations in the early universe. Unlike more familiar astrophysical black holes formed from stellar collapse, PBHs could contribute to dark matter (DM) and exhibit a wide mass range from sub-solar to tens of solar masses. The existence and nature of PBHs remain a compelling yet unresolved aspect of cosmology and gravitational physics.

Methodology and Theoretical Framework

The paper offers a comprehensive approach to modeling PBH mergers by considering two significant formation mechanisms: early universe binary formation and late-universe gravitational capture. The early universe mechanism involves PBH pairs decoupling from cosmic expansion at radiation-matter equality due to gravitational attraction. The second mechanism, more relevant in later cosmic epochs, involves PBHs losing energy to gravitational radiation during close encounters, potentially forming bound systems.

One of the novel aspects of this paper is the treatment of PBH mass functions. Instead of assuming a monochromatic distribution, the authors employ a lognormal mass function, reflecting more realistic initial conditions based on inflationary models. This choice enables the examination of a broader spectrum of masses, which better corresponds to the masses inferred from LIGO events. Precisely, the mass function parameters are tuned against known LIGO detections to assess viability and consistency with PBH merger origins.

Results and Implications

The paper demonstrates that an extended PBH mass function, specifically a lognormal distribution with certain parameters, can reconcile the merger rates detected by LIGO with the constraints on PBH abundance. For a mass function centered around 30 solar masses with a width parameter ($\sigma$) of 1, the required relative fraction of DM in PBHs is in the range of 0.0045 to 0.024, which lies within current observational constraints.

A significant insight from the analysis is the potential of an observable stochastic gravitational wave background resulting from these PBH mergers. This provides a testable prediction that links the theoretical framework to upcoming observations, particularly pertinent in the context of the LIGO sensitivity improvements over its observing runs. The anticipated GW background from PBHs within the LIGO mass range could corroborate the primordial origin hypothesis if detected in future observational data. Thus, an accurate non-detection in subsequent runs could effectively constrain or even rule out this scenario.

Cosmological Considerations

Despite the attractive proposition of PBH mergers affecting cosmological measurements, the analysis reveals that the fraction of DM converted into GWs post-recombination—a key factor that could theoretically influence the Hubble tension—is less than 1%. As such, while the theoretical framework supports PBH mergers as a valid consideration for current GW observations, the broader cosmological impact remains minimal within the confines of the assumptions and modeling.

Conclusions

The research signifies an important contribution to our comprehension of both the astrophysical sources contributing to LIGO detections and the broader interplay between DM, cosmology, and gravitational waves. By integrating extended mass functions and detailed clustering analysis, the authors prepare a fertile groundwork for confronting theory with observational advancements. Yet, uncertainties in AMR distribution, potential non-Gaussian clustering effects, and dynamics of interacting binaries remain open areas for further exploration. The dialogue between theoretical predictions and empirical constraints promises to illuminate the role of PBHs as cosmological actors in the ever-evolving tapestry of universe science.