We forecast astrophysical and cosmological parameter constraints from synergies between 21 cm intensity mapping and wide field optical galaxy surveys (both spectroscopic and photometric) over $z sim 0-3$. We focus on the following survey combinations in this work: (i) a CHIME-like and DESI-like survey in the northern hemisphere, (ii) an LSST-like and SKA I MID-like survey and (ii) a MeerKAT-like and DES-like survey in the southern hemisphere. We work with the $Lambda$CDM cosmological model having parameters ${h, Omega_m, n_s, Omega_b, sigma_8}$, parameters $v_{c,0}$ and $beta$ representing the cutoff and slope of the HI-halo mass relation in the previously developed HI halo model framework, and a parameter $Q$ that represents the scale dependence of the optical galaxy bias. Using a Fisher forecasting framework, we explore (i) the effects of the HI and galaxy astrophysical uncertainties on the cosmological parameter constraints, assuming priors from the present knowledge of the astrophysics, (ii) the improvements on astrophysical constraints over their current priors in the three configurations considered, (ii) the tightening of the constraints on the parameters relative to the corresponding HI auto-correlation surveys alone.
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