  Mapping the unresolved intensity of the 21-cm emission of neutral hydrogen
(HI) is now regarded as one the most promising tools for cosmological
investigation in the coming decades. Here, we investigate, for the first time,
extensions of the standard cosmological model, such as modified gravity and
primordial non-Gaussianity, taking self-consistently into account the present
constraints on the astrophysics of HI clustering in the treatment of the
brightness temperature fluctuations. To understand the boundaries within which
results thus obtained can be considered reliable, we examine the robustness of
cosmological parameter estimation performed via studies of 21-cm intensity
mapping, against our knowledge of the astrophysical processes leading to HI
clustering. Modelling of astrophysical effects affects cosmological observables
through the relation linking the overall HI mass in a bound object, to the mass
of the underlying dark matter halo that hosts it. We quantify the biases in
estimates of standard cosmological parameters and those describing modified
gravity and primordial non-Gaussianity, that are obtained if one misconceives
the slope of the relation between HI mass and halo mass, or the lower virial
velocity cut-off for a dark matter halo to be able to host HI. Remarkably, we
find that astrophysical uncertainties will not affect searches for primordial
non-Gaussianity - one of the strongest science cases for HI intensity mapping -
despite the signal being deeply linked to the HI bias.
