  High-number-density tracers of large-scale structure, such as the HI-rich
galaxies measured by 21 cm intensity mapping, have low sampling noise, making
them particularly promising as cosmological probes. At large scales, this
sampling noise can be subdominant to other scale-independent contributions to
the power spectrum, arising from nonlinear bias. This has important
consequences for cosmological constraints obtained from such tracers, since it
indicates that using the power spectrum does not lead to optimal constraints
even in the linear regime. In this paper, we provide a conservative estimate of
the possible improvement in constraining power of a 21cm survey if one were to
use an optimal analysis strategy (such as field-level analysis), where only the
true sampling noise enters the error budget. We find that improvements in
uncertainties on some cosmological parameters can be as large as 50%, depending
on redshift, foreground cleaning efficiency, scales used in the analysis, and
instrumental noise. One byproduct of our work is measurements of bias
parameters and stochasticity for neutral hydrogen in the IllustrisTNG
simulation over a wide range of redshifts; we provide simple fitting formulas
for these measurements. Our results motivate further exploration of new optimal
analysis techniques and provide important insights into the constraining power
of current and future 21 cm surveys.
