Constraining gravity with synergies between radio and optical cosmological surveys

In this work we present updated forecasts on parameterised modifications of gravity that can capture deviations of the behaviour of cosmological density perturbations beyond $\Lambda$CDM. For these forecasts we adopt the SKA Observatory (SKAO) as a benchmark for future cosmological surveys at radio frequencies, combining a continuum survey for weak lensing and angular galaxy clustering with an HI galaxy survey for spectroscopic galaxy clustering that can detect baryon acoustic oscillations and redshift space distortions. Moreover, we also add 21cm HI intensity mapping, which provides invaluable information at higher redshifts, and can complement tomographic resolution, thus allowing us to probe redshift-dependent deviations of modified gravity models. For some of these cases, we combine the probes with other optical surveys, such as the Dark Energy Spectroscopic Instrument (DESI) and the Vera C. Rubin Observatory (VRO). We show that such synergies are powerful tools to remove systematic effects and degeneracies in the non-linear and small-scale modelling of the observables. Overall, we find that the combination of all SKAO radio probes will have the ability to constrain the present value of the functions parameterising deviations from $\Lambda$CDM ($\mu$ and $\Sigma$) with a precision of $2.7\%$ and $1.8\%$ respectively, competitive with the constraints expected from optical surveys and with constraints we have on gravitational interactions in the standard model. Exploring the radio-optical synergies, we find that the combination of VRO with SKAO can yield extremely tight constraints on $\mu$ and $\Sigma$ ($0.9\%$ and $0.7\%$ respectively), which are further improved when the cross-correlation between intensity mapping and DESI galaxies is included.