Standard Ruler at Cosmic Dawn

The matter in our Universe comes in two flavors: dark and baryonic. Of these, only the latter couples to photons, giving rise to the well-known baryon acoustic oscillations and, in the process, generating supersonic relative velocities between dark matter and baryons. These velocities—imprinted with the acoustic scale in their genesis—impede the formation of the first stars during cosmic dawn ($z\sim 20$), modulating the expected 21-cm signal from this era. In a companion paper we showed, combining numerical simulations and analytic models, that this modulation takes the form of robust velocity-induced acoustic oscillations (VAOs), with a well-understood shape that is frozen at recombination, and unaffected by the unknown astrophysics of star formation. Here we propose using these VAOs as a standard ruler at cosmic dawn. We find that three years of 21-cm power-spectrum data from the upcoming HERA interferometer should be able to measure the Hubble expansion rate $H(z)$ at $z=15–20$ to percent-level precision, ranging from 0.3% to 11% depending on the strength of astrophysical feedback processes and foregrounds. This would provide a new handle on the expansion rate of our Universe during an otherwise unprobed epoch, opening a window to the mysterious cosmic-dawn era.

Figure 1

Measurements of the Hubble expansion rate as a function of redshift $z$. In dark purple, green, and brown we show the current constraints from BAO analyses of galaxies, quasars, and the Lyman-$\alpha$ forest, from the Baryon Oscillation Spectroscopic Survey (BOSS) [39, 40, 41, 42]. The red points show our projected measurements, obtained through 21-cm observations of the velocity-induced acoustic oscillations with HERA, under the assumptions of moderate foregrounds and regular feedback. The gray band represents the uncertainty from current CMB observations, assuming standard cosmology, which is in clear tension with the distance-ladder measurement from the Supernova $H_0$ Equation of State (SH0ES) Collaboration [50], shown in blue. Finally, the dotted-violet points correspond to forecasted BAO constraints from DESI [43], which cannot reach the redshifts probed by VAOs. In all cases the sound horizon is inferred from Planck CMB data [49].

Figure 2

The isotropic 21-cm power spectrum at $z=16.1$ as a function of wave number $k$. The black-thick line shows the result of our simulations with 21 cmvfast—assuming regular feedback strength—with clearly marked velocity-induced acoustic oscillations (VAOs). We can decompose the total signal into a VAO-only component (the dotted-purple line) and a smooth function that we marginalize over (the thin gray line), as described in Eq. (3). The VAO peaks get shifted through the Alcock-Paczynsky effect, which we illustrate with the red-dashed line, where we assumed a Hubble parameter 10% lower than our fiducial at $z=16.1$. The shown error bars have been obtained with 21 cmsense, and correspond to 540 total days of observation with HERA under the assumption of moderate foregrounds.

Figure 3

Projected $1\sigma$ and $2\sigma$ confidence contours for $H(z)r_d$ and $D_A(z)/r_d$ at $z=18$, normalized to their fiducial values, under two different foreground models: moderate (red) and optimistic (blue), assuming regular feedback in both cases. The black-dashed degeneracy line has a fixed isotropic AP parameter [77], and the green lines mark the fiducial values of unity for reference.