Intensity mapping of post-reionization 21-cm signal and its cross-correlations as a probe of $f(R)$ gravity

We propose the intensity mapping of the redshifted HI 21-cm signal from the post-reionization epoch as a cosmological probe of $f(R)$ gravity. We consider the Hu-Sawicki class of $f(R)$ gravity models characterized by a single parameter $f_{,R0}$. The $f(R)$ modification to gravity affects the post-reionization $21$-cm power spectrum through the change in the growth rate of density fluctuations. We find that a radio interferometric observation with a SKA1-Mid like radio telescope in both auto-correlation and cross-correlation with galaxy weak-lensing and Ly-$\alpha$ forest may distinguish $f(R)$ models from $LCDM$ cosmology at a precision which is competitive with other probes of $f(R)$ gravity.