How baryons can significantly bias cluster count cosmology
  We quantify two main pathways through which baryonic physics biases cluster
count cosmology. We create mock cluster samples that reproduce the baryon
content inferred from X-ray observations. We link clusters to their
counterparts in a dark matter-only universe, whose abundances can be predicted
robustly, by assuming the dark matter density profile is not significantly
affected by baryons. We derive weak lensing halo masses and infer the
best-fitting cosmological parameters $\Omega_\mathrm{m}$,
$S_8=\sigma_8(\Omega_\mathrm{m}/0.3)^{0.2}$, and $w_0$ from the mock cluster
sample. We find that because of the need to accommodate the change in the
density profile due to the ejection of baryons, weak lensing mass calibrations
are only unbiased if the concentration is left free when fitting the reduced
shear with NFW profiles. However, even unbiased total mass estimates give rise
to biased cosmological parameters if the measured mass functions are compared
with predictions from dark matter-only simulations. This bias dominates for
haloes with $m_\mathrm{500c} < 10^{14.5} \, h^{-1} \, \mathrm{M_\odot}$. For a
stage IV-like cluster survey without mass estimation uncertainties, an area
$\approx 15000 \, \mathrm{deg^2}$ and a constant mass cut of
$m_\mathrm{200m,min} = 10^{14} \, h^{-1} \, \mathrm{M_\odot}$, the biases are
$-11 \pm 1 \, \%$ in $\Omega_\mathrm{m}$, $-3.29 \pm 0.04 \, \%$ in $S_8$, and
$9 \pm 1.5 \, \%$ in $w_0$. The statistical significance of the baryonic bias
depends on how accurately the actual uncertainty on individual cluster mass
estimates is known. We suggest that rather than the total halo mass, the
(re-scaled) dark matter mass inferred from the combination of weak lensing and
observations of the hot gas, should be used for cluster count cosmology.
