Gravitational Wave Informed Inference of 21-cm Global Signal Parameters

TL;DR

The study introduces a multi-messenger framework that leverages next-generation gravitational-wave detectors to constrain the high-redshift star formation rate density via binary black hole mergers and uses this information to sharpen inference of the 21-cm global signal during the Cosmic Dawn. By modeling the 21-cm signal with parameters for SFRD, Ly$\alpha$ coupling, and X-ray heating, and linking BBH merger rates to the SFRD through hierarchical inference, the authors demonstrate that GW observations can substantially reduce degeneracies in the 21-cm signal parameters. Fisher-matrix–based GW constraints on $D_L$ inform priors on $\Psi_0$ and $\beta$, which in turn tighten the posteriors for the 21-cm parameters $\Psi_0$, $\beta$, $\log f_{\alpha}$, and $\log f_{Xh}$ when analyzed jointly, achieving improvements beyond 21-cm data alone. This proof-of-principle showcases a viable path for integrating GW and 21-cm observations to illuminate the timing and nature of the Cosmic Dawn and the early star-formation history.

Abstract

Understanding how and when the first stars and galaxies formed remains one of the central challenges in modern cosmology. These structures emerged during the transition from the Dark Ages to the Cosmic Dawn, a period that remains observationally unconstrained despite strong theoretical progress. During this epoch, neutral hydrogen absorbed a fraction of cosmic microwave background photons through its 21-cm hyperfine transition, producing a 21-cm absorption signal whose evolution encodes the early Universe's thermal and ionization history. However, extracting the underlying astrophysical parameters from this signal is limited by severe parameter degeneracies, which cannot be resolved without independent observational probes. The next-generation gravitational wave (GW) detectors, such as Cosmic Explorer (CE), will observe binary black hole (BBH) mergers up to very large redshifts and hence will detect a fraction of them formed within the redshift range $\sim 13-25$. The merger rate of these BBHs will depend on the star formation rate density (SFRD) at these redshifts, together with the BBH formation efficiency and a time delay distribution. Therefore, the merger rate of these BBHs can work as a tracer of the SFRD in the redshift range $\sim 13-25$. In this Letter, we establish a novel multi-messenger framework and present a proof-of-principle concept of how the observations of BBH mergers form next-generation GW detectors can improve the inference of parameters generating the 21-cm cosmic hydrogen signal, and help break degeneracies between them.

Figures (4)

• Figure 1: The 21-cm global signal for a fiducial SFRD of the form $\Psi = \Psi_0 e^{-\beta (z - z_0)}$. The redshift range is taken to be $z\sim13-25$. Other parameters are set to $\Psi_0 = 0.0066 \, M_{\odot} \rm Mpc^{-3} yr^{-1}$, $\beta = 4/5$, $z_0 = 17$, $f_{\alpha} = 6 \times 10^{37}$, $f_{Xh} = 3 \times 10^{-2}$. A Gaussian instrumental noise of standard deviation $\Delta T_b = 10 \, \rm mK$ has been added to the signal.
• Figure 2: The $1d$-posteriors of the SFRD parameters inferred exclusively by GW hierarchical inference on 100 (blue) and 1000 (brown) BBH events. The black dashed lines represent the true values, while the light blue and brown shaded regions represent the 90% credible intervals.
• Figure 3: Top panel: The $1d$-posteriors of the 21-cm global signal parameters using only the data from the 21cm observation, with no complementary GW information. Bottom panel: The inferred posteriors of 21-cm global signal parameters obtained using both the 21-cm signal observation, as well as the GW hierarchical inference results shown in Figure \ref{['fig: gw_post']}. Blue histograms correspond to inference involving 100 GW events, while the brown histograms correspond to 1000 GW events. The black dashed line and the light shaded regions have the same meaning as in Figure \ref{['fig: gw_post']}.
• Figure 4: The inferred posteriors of 21-cm global signal parameters obtained using the GW hierarchical inference posteriors as priors (see Figure \ref{['fig: gw_post']}). The 100 GW-events case is assumed here. The black dashed line represents the $5th$, $50th$, and $95th$ percentiles, the orange lines represent the true values, the blue lines represent the priors, while the $2d$-contours correspond to $68\%$ and $90\%$ credible regions.