Calibrating spectral siren cosmology with synthetic catalogs of binary black hole mergers

Abstract

Binary black hole (BBH) mergers detected through Gravitational Waves (GWs) are a promising probe for the cosmic expansion. These sources are standard sirens for which we can directly measure the luminosity distance, but their redshift is degenerate with the determination of their source masses. In analogy to standard candles, the redshift of standard sirens can be obtained using a calibration based on the source mass spectrum, but without the need for a cosmological ladder. It has been recently shown that a mismodeling of the BBH mass spectrum is very likely to introduce a bias in the determination of the Hubble constant. To tackle this issue, we develop a BBH population model based on Normalizing Flows, trained on synthetic BBH catalogs generated from astrophysical prescriptions, including binaries formed through both isolated stellar evolution and dynamical environments. We validate this approach with a mock BBH dataset, demonstrating that the Normalizing Flow framework faithfully recovers the true distribution and eliminates systematic biases in the Hubble constant inference. By using this model on GWTC-4.0 data, we obtain $H_0 = 71.62^{+4.04}_{-4.00}\; km \; s^{-1} Mpc^{-1}$ at 68.3% credible interval. Assuming the astrophysical prescriptions present in B-POP, we also show that the determination of $H_0$ is degenerate with the fraction of binaries born in the dynamical and isolated formation channel, with a Planck cosmology favouring $\sim 35\%$ binaries formed in the dynamical environment while a SH0ES cosmology favouring a value of $\sim 25\%$.

Figures (8)

• Figure 1: Astrophysical distribution of the mock BBH source-frame drawn from the Power Law + Evolving Peak population, used to benchmark the model. The plot is shown in the $\log m_1 - z$ plane, where the dots are samples drawn from the redshift-evolving distribution. Contour lines enclose the 68% and 90% density regions. The dashed line shows the linear redshift evolution of the mean of the Gaussian Peak: $\mu(z) = z \; \mu_{z_1} + \mu_{z_0}$. The top and right panels show the corresponding marginal distributions.
• Figure 2: Posterior distributions of $H_0$ inferred using the mock GW catalog under two different population assumptions. The purple posterior is obtained when masses are modeled with the phenomenological Power Law + Peak that does not evolve with redshift: the injected value of $H_0$ (vertical dashed line) falls outside the 99.7% C.I. of the inferred posterior. The magenta posterior shows inference results obtained using Normalizing Flows to fit the redshift-evolving population: the evolution is well captured and the injected $H_0$ value is recovered.
• Figure 3: Corner plot showing the joint distribution of BBH masses and merger redshift for the two mock populations. Blue and orange contours (enclosing the 68.3% and 90% credible regions) and smoothed KDE curves represent the normalizing flow fits for the Power Law and the Evolving Peak, respectively. Grey histograms, shown only in the one-dimensional marginals, correspond to samples drawn from the mock redshift-evolving catalog. The Normalizing Flows accurately recover the underlying mass and redshift distributions for both channels.
• Figure 4: Redshift evolution of the primary BBH mass distribution in the synthetic astrophysically simulated B-pop catalog. Each curve shows the distribution of $\log (m_1/M_\odot)$ within a redshift bin. The population has a complex, multimodal structure and a strong redshift dependence. This complex behavior cannot be modeled with analytical phenomenological laws but can be captured using Normalizing Flows.
• Figure 5: Corner plot showing the joint distribution of BBH primary and secondary masses and merger redshift for the two formation channels. Blue and orange contours (that enclose the 68.3% and 90% credible regions) and smoothed kde curves show the normalizing flow fits of the isolated binary and dynamical channels, respectively. Grey histograms show the B-pop population samples and are shown only in the one-dimensional marginals. The Normalizing Flows fits correctly recover the mass and redshift spectra for both channels.