Measuring the cosmic expansion rate using 21-cm velocity acoustic oscillations

The fluctuations in the dark matter-baryon relative velocity field are imprinted as acoustic oscillations in the 21-cm power spectrum during cosmic dawn (CD). These velocity acoustic oscillations (VAOs) keep the imprints of the comoving sound horizon scale. In a previous work by Mu\~noz, it has been demonstrated that these VAOs can be treated as standard rulers to measure the cosmic expansion rate at high redshifts by considering a variety of Lyman-Werner feedback strengths and foreground contamination scenarios. Here we extend that analysis by using a modified version of the public code \texttt{21cmFAST}. We use this code to simulate the VAOs in 21-cm power spectrum and forecast the potential to constrain $H(z)$ with the HERA radio telescope, taking into account the effects of Lyman-$\alpha$ heating, Lyman-Werner feedback and foregrounds, the dependence on various astrophysical parameters, and the degeneracy with cosmological parameters. We find that $H(z)$ can be measured with HERA at $\sim 0.3-6\%$ relative accuracy in the range $11 < z < 20$, under different astrophysical and foreground scenarios, with uncertainties in the Planck cosmological parameters setting a $\sim 0.08-0.2\%$ relative-error floor in the measurement. This accuracy is on par with most low-redshift measurements and can be helpful in testing various cosmological scenarios motivated by the ongoing ``Hubble Tension".