REVIEW
Confronting the primordial black hole scenario with the gravitational-wave events detected by LIGO-Virgo
Cosmology and Nongalactic Astrophysics · Submitted 26 Aug 2021 · 83 references
Pith's verdict: A competent GWTC-3 update to the PBH population fit, with a useful event-by-event rate table, but the fit assumes every LIGO-Virgo binary is primordial and never says so.
T0 · AI review
Why Pith says this
Highlight any text to comment on it.
Referee report
The paper
The paper claims
The authors reconstruct the mass distribution of primordial black holes directly from the LIGO-Virgo catalog, argue that the result matches a broad, red-tilted spectrum of curvature perturbations, and use the same distribution to test which
The reading
What carries the argument
Three pieces carry the argument. First, the binned mass function of Eq. (1), a step function on five mass intervals normalised to unity, which lets the data choose the shape instead of a parametric form. Second, the primordial binary merger rate of Eq. (2), $R_{12}(t) ≈ 2.8×10^6,(t/t_0)^{-34/37} f_{PBH}^2(0.7f_{PBH}^2+σ_{eq}^2)^{-21/74}×…$, which converts a mass function and a dark-matter fraction into a comoving merger rate and is what makes the event-by-event comparison in Table I possible. Third, the mapping from a curvature power spectrum to a mass function: Press-Schechter integration of a Gaussian density-contrast PDF above a threshold $δ_c ≈ 0.45$, the critical-collapse relation $m = M_Hκ(δ_m-δ_c)^{γ}$ with $κ=3.3$, $γ=0.36$, the non-linear relation $δ_m = δ_ζ - 3δ_ζ^2/8$, and a QCD-era equation of state that lowers $δ_c$ and so raises the abundance near $1M_⊙$. The same power spectrum is then fed into the standard second-order kernel of Eq. (17) to produce the scalar-induced gravitational-wave spectrum, which is why the background prediction is not an add-on but a consequence of the fit.
Extended reading notes
Core claim
The central claim is that the binary black hole mass distribution inferred from GWTC-3 is compatible with a purely primordial origin, and that this distribution has a physical explanation in a broad red-tilted spectrum of curvature perturbations. The reconstruction is deliberately shape-agnostic: five mass bins between $1M_⊙$ and $130M_⊙$, four free heights, plus $f_{PBH}$, fitted with the inhomogeneous-Poisson likelihood of Eq. (3) using the primordial binary merger rate of Eq. (2). Case I (events with non-vanishing effective spin discarded) gives $P_1 = 1.5^{+0.6}_{-0.7}×10^{-1},M_⊙^{-1}$, $P_2 = 2.5^{+1.8}_{-1.1}×10^{-2},M_⊙^{-1}$, $P_3 = 1.4^{+0.4}_{-0.3}×10^{-2},M_⊙^{-1}$, $P_4 = 2.0^{+0.9}_{-0.7}×10^{-3},M_⊙^{-1}$ and $f_{PBH} = 2.9^{+0.7}_{-0.6}×10^{-3}$; case II gives similar values with $f_{PBH} = 3.4^{+0.7}_{-0.5}×10^{-3}$. Feeding that shape through a Press-Schechter calculation with critical collapse, the non-linear density-curvature relation, and a QCD-era equation of state yields a broad red-tilted spectrum with $A = 0.004647$, $α = -0.1033$ (case I) that traces the reconstructed bins, including the enhancement near $1M_⊙$ produced by the QCD transition. The event-by-event comparison in Table I is the sharp end of the claim: GW190521's primordial rate, $0.12^{+0.11}_{-0.07},Gpc^{-3},yr^{-1}$, matches the LIGO-Virgo rate $0.13^{+0.30}_{-0.11}$, whereas GW190425, GW190814, GW200105 and GW200115 come out at $3.6$, $0.13$, $1.9$ and $6.3,Gpc^{-3},yr^{-1}$ against quoted rates of $460$, $7$, $16$ and $36$. The authors conclude that the light components in those four events are neutron stars or other compact objects, not primordial black holes, and that the same mass function predicts a stochastic background from primordial binaries plus inevitable scalar-induced gravitational waves, both within current limits and within reach of LISA, Taiji, TianQin, ET, CE, NEMO and FAST.
Load-bearing premise
The likelihood contains only the primordial binary merger rate and no astrophysical black hole component, so every GWTC-3 binary black hole retained in the sample is treated as primordial; if most of them formed from stellar collapse, the reconstructed bins are not a primordial mass function and the event-by-event rate comparisons lose their meaning.
Editorial extensions
If this is right
- GW190521's primary mass, inside the pair-instability gap where stellar collapse is not expected to reach, is accounted for by a primordial binary merger without invoking a stellar channel.
- The light companion in GW190814, GW190425, GW200105 and GW200115 is pushed toward a neutron-star or exotic-object interpretation, since the primordial rate for those masses is one to two orders of magnitude below the LIGO-Virgo rate.
- The stochastic background from primordial binary coalescences, computed for both spin cases, should be measurable by ET, CE, NEMO, LISA, Taiji and TianQin while staying under the LIGO O3 limit.
- The scalar-induced gravitational-wave signal tied to the same curvature spectrum falls in the nanohertz band, consistent with the NANOGrav 12.5-year data and within reach of FAST.
- A single broad red-tilted curvature spectrum with $α ≈ -0.10$ and $A ≈ 0.0046$ links the dark-matter fraction, the binary mass function, and two independent gravitational-wave backgrounds.
Reading between the lines
- The analysis fits a primordial-only population; a mixed fit with an astrophysical binary black hole component would test whether the reconstructed bins survive, since a stellar sub-population peaking near $10M_⊙$ could mimic the falling shape the authors attribute to the curvature spectrum.
- The QCD-transition enhancement near $1M_⊙$ is a genuine prediction rather than a fit: a future detector measuring the sub-solar mass function shape would either confirm the bump's location and width or show it is absent.
- Because the same $P_R(k)$ fixes both the binary merger background and the scalar-induced background, a joint detection or non-detection across the LISA and pulsar-timing bands would over-constrain the two-parameter spectrum $(A, α)$ far more tightly than either band alone.
- The event-level rate comparison depends on the quoted LIGO-Virgo rates, which for GW190425 carry a factor-of-two uncertainty; as those rate estimates tighten, the light-mass exclusion strengthens or weakens accordingly.
Original abstract
Adopting a binned method, we model-independently reconstruct the mass function of primordial black holes (PBHs) from GWTC-3 and find that such a PBH mass function can be explained by a broad red-tilted power spectrum of curvature perturbations. Even though GW190521 with component masses in upper mass gap $(m>65M_\odot)$ can be naturally interpreted in the PBH scenario, the events (including GW190814, GW190425, GW200105, and GW200115) with component masses in the light mass range $(m<3M_\odot)$ are quite unlikely to be explained by binary PBHs although there are no electromagnetic counterparts because the corresponding PBH merger rates are much smaller than those given by LIGO-Virgo. Furthermore, we predict that both the gravitational-wave (GW) background generated by the binary PBHs and the scalar-induced GWs accompanying the formation of PBHs should be detected by the ground-based and space-borne GW detectors and pulsar timing arrays in the future.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
Adopting a binned method, we model-independently reconstruct the mass function of primordial black holes (PBHs) from GWTC-3 and find that such a PBH mass function can be explained by a broad red-tilted power spectrum of curvature perturbations. Even though GW190521 with component masses in upper mass gap $(m>65M_\odot)$ can be naturally interpreted in the PBH scenario, the events (including GW190814, GW190425, GW200105, and GW200115) with component masses in the light mass range $(m<3M_\odot)$ are quite unlikely to be explained by binary PBHs although there are no electromagnetic counterparts because the corresponding PBH merger rates are much smaller than those given by LIGO-Virgo. Furthermore, we predict that both the gravitational-wave (GW) background generated by the binary PBHs and the scalar-induced GWs accompanying the formation of PBHs should be detected by the ground-based and space-borne GW detectors and pulsar timing arrays in the future.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Adopting a binned method, we model-independently reconstruct the mass function of primordial black holes (PBHs) from GWTC-3 and find that such a PBH mass function can be explained by a broad red-tilted power spectrum of curvature perturbations. | contribution 0.50 | 0.96 | 0.56 | asserted 0.92 |
| s1 | Even though GW190521 with component masses in upper mass gap $(m>65M_\odot)$ can be naturally interpreted in the PBH scenario, the events (including GW190814, GW190425, GW200105, and GW200115) with component masses in the light mass range $(m<3M_\odot)$ are quite unlikely to be explained by binary PBHs although there are no electromagnetic counterparts because the corresponding PBH merger rates are much smaller than those given by LIGO-Virgo. | result 0.79 | 0.64 | 0.38 | asserted 0.78 |
| s2 | Furthermore, we predict that both the gravitational-wave (GW) background generated by the binary PBHs and the scalar-induced GWs accompanying the formation of PBHs should be detected by the ground-based and space-borne GW detectors and pulsar timing arrays in the future. | result 0.43 | 0.70 | 0.16 | asserted 0.58 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Figures reproduced from arXiv:2108.11740 by the authors.
References
How the literature uses it
54 arXiv papers cite this in 68 sentences
Papers citing it · 38 sentences without a confident label
Contests it 1 paper
-
This constraint was not included in Ref. [ref] , where the fit was arbitrarily cut at $≈M_⊙$ and no constraining power from the absence of subsolar mergers is included in the inference.
From inflation to black hole mergers and back again: Gravitational-wave data-driven constraints on inflationary scenarios with a first-principle model of primordial black holes across the QCD epoch · Introduction · contest 0.75
Uses its method or tool 1 paper
-
Accordingly, the hyper-likelihood $ℒ(𝐡 | Φ_m, γ,κ,z_pk, v_0 , R_0)$ related to the single-event likelihood $ℒ(h_i | θ)$ for the $i$-th event can be written as [ref] [equation] where $ξ(Φ_m,γ, κ,z_pk, v_0)$ is the detection fraction that quantifies selection biases for a population based on hyperparameters $(Φ_m,γ, κ,z_pk, v_0)$, described as [equation] The detection probability based on the source parameters $θ$ is $P_det(θ)$, which is related to the simulated signals.
Constraints on peculiar velocity distribution of binary black holes using gravitational waves with GWTC-3 · Hierarchical Bayesian inference · 0.93
Compares with it 1 paper
-
The results of the local merger rate and abundance of PBHs are consistent with the previous estimations [ref] , confirming that CDM cannot be dominated by the stellar-mass PBHs.
Constraining the Merger History of Primordial-Black-Hole Binaries from GWTC-3 · Critical collapse mass function · 0.86
Cites it as background 22 papers
-
Calculation of the merger rate from binary PBHs (BPBHs) and comparison with the value inferred from experiment has been performed in the context of early- and late-time Universe BPBHs [ref] and constraints on the abundance of PBHs have been set to respect the observed rates of GW detections [ref] (see [ref] for reviews).
Primordial black hole mergers from three-body interactions · Introduction · 0.88
-
Although the SGWB from SMBHBs is supposed to be the most promising source for the signal detected by the PTAs, the signal at nanoHertz can also originate from some cosmological processes [ref] , such as cosmological first-order phase transition [ref] , cosmic strings [ref] , domain walls [ref] , and scalar-induced GW [ref] accompanying the formation of primordial black holes [ref] .
Cosmological Interpretation for the Stochastic Signal in Pulsar Timing Arrays · Introduction · 0.95
-
Besides the astrophysical black holes, another possible explanation for the LVK BBHs is the primordial black holes (PBHs) [ref] .
Constraining the Merger History of Primordial-Black-Hole Binaries from GWTC-3 · Introduction · 0.88
What it cites · 41 sentences without a confident label
Uses the method or tool of 12 papers
-
Given the data of $N$ binary BH (BBH) detections, $= (d_1, …, d_N)$, the likelihood for an inhomogeneous Poisson process is [ref] p(|, R) ∝e^-β() ∏_i^N ∫ p(|d_i) _12(|), where $≡{m_1, m_2}$, $p(|d_i)$ is the posterior of an individual event, and $β() ≡∫ VT() _12(|)$ where $VT()$ is the spacetime sensitivity volume of detectors.
Does the Black Hole Merger Rate Evolve with Redshift? · Introduction · 0.99
-
Given the data of $N$ binary BH (BBH) detections, $= (d_1, …, d_N)$, the likelihood for an inhomogeneous Poisson process is [ref] p(|, R) ∝e^-β() ∏_i^N ∫ p(|d_i) _12(|), where $≡{m_1, m_2}$, $p(|d_i)$ is the posterior of an individual event, and $β() ≡∫ VT() _12(|)$ where $VT()$ is the spacetime sensitivity volume of detectors.
Extracting distribution parameters from multiple uncertain observations with selection biases · Introduction · 0.99
-
Given the data of $N$ binary BH (BBH) detections, $= (d_1, …, d_N)$, the likelihood for an inhomogeneous Poisson process is [ref] p(|, R) ∝e^-β() ∏_i^N ∫ p(|d_i) _12(|), where $≡{m_1, m_2}$, $p(|d_i)$ is the posterior of an individual event, and $β() ≡∫ VT() _12(|)$ where $VT()$ is the spacetime sensitivity volume of detectors.
Reconstructing phenomenological distributions of compact binaries via gravitational wave observations · Introduction · 0.99
Uses data or values from 13 papers
-
We adopt a binned method to model-independently reconstruct the PBH mass function from GWTC-3 [ref] , and we find that GW190521 can be explained by a binary PBH merger.
GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run · Introduction · 0.97
-
The PBH mass $m$ is related to the density contrast by the critical collapse, namely $m=M_H κ(δ_m-δ_c)^γ$ [ref] with $κ=3.3$ and $γ=0.36$ [ref] .
Critical behaviour in gravitational collapse of radiation fluid --- A renormalization group (linear perturbation) analysis --- · Introduction · 0.97
-
The PBH mass $m$ is related to the density contrast by the critical collapse, namely $m=M_H κ(δ_m-δ_c)^γ$ [ref] with $κ=3.3$ and $γ=0.36$ [ref] .
Near-Critical Gravitational Collapse and the Initial Mass Function of Primordial Black Holes · Introduction · 0.97
Compares with 5 papers
-
The corresponding GWBs for case I and case II are respectively shown as the blue and red band in ogw, indicating that both of them are compatible with the current limits given by LIGO O3 [ref] , and should be detected by the future ground-based and space-borne GW detectors, such as Neutron Star Extreme Matter Observatory (NEMO) [ref] , Cosmic Explorer (CE) [ref] , Einstein Telescope (ET) [ref] , Taiji [ref] , TianQin [ref] and LISA [ref] .
Exploring the Sensitivity of Next Generation Gravitational Wave Detectors · Introduction · 0.80
-
The corresponding GWBs for case I and case II are respectively shown as the blue and red band in ogw, indicating that both of them are compatible with the current limits given by LIGO O3 [ref] , and should be detected by the future ground-based and space-borne GW detectors, such as Neutron Star Extreme Matter Observatory (NEMO) [ref] , Cosmic Explorer (CE) [ref] , Einstein Telescope (ET) [ref] , Taiji [ref] , TianQin [ref] and LISA [ref] .
TianQin: a space-borne gravitational wave detector · Introduction · 0.80
-
The corresponding GWBs for case I and case II are respectively shown as the blue and red band in ogw, indicating that both of them are compatible with the current limits given by LIGO O3 [ref] , and should be detected by the future ground-based and space-borne GW detectors, such as Neutron Star Extreme Matter Observatory (NEMO) [ref] , Cosmic Explorer (CE) [ref] , Einstein Telescope (ET) [ref] , Taiji [ref] , TianQin [ref] and LISA [ref] .
Laser Interferometer Space Antenna · Introduction · 0.80
Cites as background 12 papers
-
The GWB associated with PBHs includes two main contributions: one is the coalescences of binary PBHs [ref] (see more discussion in [ref] ) and the other is SIGW inevitably generated by the curvature perturbations during the formation of PBHs [ref] .
Stochastic Gravitational-Wave Background from Binary Black Holes and Binary Neutron Stars and Implications for LISA · Introduction · 0.90
-
The GWB associated with PBHs includes two main contributions: one is the coalescences of binary PBHs [ref] (see more discussion in [ref] ) and the other is SIGW inevitably generated by the curvature perturbations during the formation of PBHs [ref] .
Gravitational wave background as a probe of the primordial black hole abundance · Introduction · 0.90
-
The GWB associated with PBHs includes two main contributions: one is the coalescences of binary PBHs [ref] (see more discussion in [ref] ) and the other is SIGW inevitably generated by the curvature perturbations during the formation of PBHs [ref] .
Can we distinguish astrophysical from primordial black holes via the stochastic gravitational wave background? · Introduction · 0.90
Discussion
Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.