Abstract
We reconsider the Alcock–Paczyński effect on 21-cm fluctuations from high redshift, focusing on the 21-cm power spectrum. We show that at each accessible redshift both the angular diameter distance and the Hubble constant can be determined from the power spectrum, at epochs and on scales where the ionized fraction fluctuations are linear. Furthermore, this is possible using anisotropies that depend only on linear density perturbations and not on astrophysical sources of 21-cm fluctuations. We show that measuring these quantities at high redshift would not just confirm results from the cosmic microwave background (CMB); if the 21-cm power spectrum can be measured to better than 10 per cent precision, it will improve constraints from the CMB alone on cosmological parameters including dark energy.
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