Constraining the Hubble parameter with the 21-cm brightness temperature signal in a universe with inhomogeneities

We consider the 21-cm brightness temperature as a probe of the Hubble tension in the framework of an inhomogeneous cosmological model. Employing Buchert's averaging formalism to study the effect of inhomogeneities on the background evolution, we consider scaling laws for the backreaction and curvature consistent with structure formation simulations. We calibrate the effective matter density using Markov chain Monte Carlo analysis using Union 2.1 Supernova Ia data. Our results show that a higher Hubble constant ($\ensuremath{\sim}73\text{ }\text{ }\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$) leads to a shallower absorption feature in the brightness temperature versus redshift curve. On the other hand, a lower value ($\ensuremath{\sim}67\text{ }\text{ }\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$) produces a remarkable dip in the brightness temperature ${T}_{21}$. Such a substantial difference is absent in the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. Our findings indicate that inhomogeneities could significantly affect the 21-cm signal, and may shed further light on the different measurements of the Hubble constant.