Probing f(R) gravity using the post-reionization HI 21-cm signal
  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 family 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. The quantity of interest is the redshift space distortion
parameter $\beta_T(k, z)$ which imprints the change. We find that a radio
interferometric observation at an observing frequency $710$MHz with a SKA-1-Mid
like radio telescope may measure the binned $\beta_T(k)$ at a level of
sensitivity to distinguish $f(R)$ models with $\log_{10} |f_{,R0}| > -5$ at a
$> 5-\sigma$ level in the k range $ k > 0.4 MPc^{-1}$. We find that using a
Fisher matrix analysis the $68\%$ bound obtained on the parameter is $ -5.62 <
\log_{10} |f_{,R0}| < - 4.38$ which is competitive with other probes of f(R)
gravity. Thus the future observation of the post-reionization HI signal holds
the potential to put robust constraints on f(R) gravity models and enrich our
understanding of late time cosmic evolution and structure formation.
