The Stochastic Siren: Astrophysical Gravitational-Wave Background Measurements of the Hubble Constant

Abstract

We report the first measurement of the Hubble constant $H_0$ using the stochastic gravitational-wave background arising from binary black hole mergers. This astrophysical background is sensitive to the expansion history of the Universe and thus can be used for cosmological parameter inference independently of not only electromagnetic methods, but also gravitational-wave standard siren approaches. We describe the background's cosmological dependence and show how it can be used as a ``stochastic siren'' to measure $H_0$. By analyzing existing resolved binary black hole mergers and the current non-detection of the background, we find that $H_0$ can be measured more accurately relative to using resolved mergers alone. We also note that the stochastic siren may serve a unique role in the Hubble tension in that the lower bound of the $H_0$ measurement would progressively increase with continued non-detection of the background.

Figures (11)

• Figure 1: Posterior distributions of the Hubble constant obtained with the spectral siren ($\mathcal{L}_\mathrm{FG}$, dashed blue), the GWB search ($\mathcal{L}_\mathrm{BG}$, dotted orange), and the stochastic siren joint measurement ($\mathcal{L}_\mathrm{joint}$, red), each respectively marginalized over their 14 other parameters. Since no GWB has been detected, $\mathcal{L}_\mathrm{BG}$ shows less support for lower values of $H_0$. Combining this with the foreground shifts the posterior, as indicated by the maximum a-posteriori probabilities for $\mathcal{L}_\mathrm{FG}$ and $\mathcal{L}_\mathrm{joint}$ shown by $\times$ markers (no marker is shown for $\mathcal{L}_\mathrm{BG}$ since the GWB non-detection provides only a lower bound on $H_0$). The joint measurement shifts slightly closer to the Hubble tension region vertically demarcated by the Planckaghanim2020planck and SH0ES Riess:2021jrx values.
• Figure 2: Redshift model hyperparameters, together with cosmological parameters, as inferred via the BBH spectral siren ($\mathcal{L}_\mathrm{FG}$, blue) and stochastic siren ($\mathcal{L}_\mathrm{joint}$, red) methods. Observe that most hyperparameters do not demonstrate an improvement with the current non-detection of the BBH GWB, with the exception of $\gamma$ as elaborated in the text.
• Figure 3: Mass model hyperparameters, together with cosmological parameters, as inferred via the BBH spectral siren ($\mathcal{L}_\mathrm{FG}$, blue) and stochastic siren ($\mathcal{L}_\mathrm{joint}$, red) methods. Observe that effectively no mass hyperparameter constraints demonstrate an improvement with the current non-detection of the BBH GWB.
• Figure 4: The time to detect a GWB with a detector network consisting of LIGO-Hanford, LIGO-Livingston, and Virgo with the sensitivity of aLIGO, A#, or Voyager. In all plots, the dashed lines represent SNR values of three, eight, and twelve respectively, and results are shown for both the Planck aghanim2020planck and SH0ES Riess:2021jrx values of $H_0$ to give an example for how time to detection changes with $H_0$. Note that the time to detection is very different across these different networks, so these plots have a different scaling on the x-axis.
• Figure 5: SNR of the GWB for various future detector networks as a function of two cosmological parameters ($H_0$ with either $\Omega_{m,0}$ or $w_0$), with the other 13 (hyper)parameters fixed to values denoted in the text. Top (middle) plots: a network of three A# detectors after one year (two years) of observation, with SNR shown as a heatmap. Contour lines illustrate constant values of $\mathrm{SNR}=8$ and $\mathrm{SNR}=20$, while the red horizontal and vertical lines indicate existing cosmological parameter measurements. Observe that regions of parameter space that are detectable (areas with higher SNR) expand with increasing observing time, such that the GWB would be detectable within 1-2 years. Bottom: the same as the previous plots, but for networks with aLIGO, A#, and Voyager sensitivities after two years of observation. Observe that there are effectively no values of these parameters that would make the GWB measurable in aLIGO after only two years. Analogous plots that pair $H_0$ with population hyperparameters are shown in the remainder of this text.