Redshift-space 21-cm bispectrum multipoles as an SKA-era gravity test in the post-reionization Universe

The redshifted 21-cm line from neutral hydrogen ($\textrm{H}\textsc{i}$) enables volumetric intensity mapping of large-scale structure in the post-reionization Universe. In anticipation of \texttt{SKA-MID}'s wide redshift coverage and high signal-to-noise clustering measurements, we study the redshift-space 21-cm bispectrum and its spherical-harmonic multipoles as probes of anisotropic non-linear structure formation and departures from General Relativity. Using a tree-level perturbative description for the 21-cm brightness-temperature field in redshift space, and adopting the Hu--Sawicki $f(R)$ model as a representative modified-gravity scenario, we forecast the detectability of configuration-dependent signatures with an \texttt{SKA-MID}--like survey. We derive the bispectrum-multipole covariance including sample variance and thermal noise and evaluate the expected signal-to-noise of deviations relative to $\Lambda$CDM. We find that the observable information is dominated by the lowest multipoles, while higher-order modes are strongly suppressed. This concentration in the lowest multipoles is well matched to \texttt{SKA-MID} sensitivity and to the quasi-linear modes that are expected to remain accessible in practice. The strongest modified-gravity sensitivity arises from squeezed and stretched triangle configurations on quasi-linear scales, where scale-dependent growth enhances the bispectrum relative to the total variance. Our results position 21-cm bispectrum multipoles as a practical, SKA-ready observable for testing gravity beyond $\Lambda$CDM in the post-reionization epoch.