We use a set of hydrodynamical (Hydro) and dark matter only (DMonly) simulations to calibrate the halo mass function (HMF). We explore the impact of baryons, propose an improved parametrization for spherical overdensity masses and identify difference
s between our DMonly HMF and previously published HMFs. We use the textit{Magneticum} simulations, which are well suited because of their accurate treatment of baryons, high resolution, and large cosmological volumes of up to $(3818~textrm{Mpc})^3$. Baryonic effects globally decrease the masses of galaxy clusters, which, at a given mass, results in a decrease of their number density. This effect vanishes at high redshift $zsim2$ and for high masses $M_{200textrm m}gtrsim10^{14}Modot$. We perform cosmological analyses of three idealized approximations to the cluster surveys by the South Pole Telescope (SPT), textit{Planck}, and eROSITA. We pursue two main questions: (1) What is the impact of baryons? -- For the SPT-like and the textit{Planck}-like samples, the impact of baryons on cosmological results is negligible. In the eROSITA-like case, however, neglecting the baryonic impact leads to an underestimate of $Omega_textrm m$ by about $0.01$, which is comparable to the expected uncertainty from eROSITA. (2) How does our DMonly HMF compare with previous work? -- For the textit{Planck}-like sample, results obtained using our DMonly HMF are shifted by $Delta(sigma_8)simeqDelta(sigma_8(Omega_textrm m/0.27)^{0.3})simeq0.02$ with respect to results obtained using the Tinker et al. (2008) fit. This suggests that using our HMF would shift results from textit{Planck} clusters toward better agreement with CMB anisotropy measurements. Finally, we discuss biases that can be introduced through inadequate HMF parametrizations that introduce false cosmological sensitivity.
We present a velocity dispersion-based mass calibration of the South Pole Telescope Sunyaev-Zeldovich effect survey (SPT-SZ) galaxy cluster sample. Using a homogeneously selected sample of 100 cluster candidates from 720 deg2 of the survey along with
63 velocity dispersion ($sigma_v$) and 16 X-ray Yx measurements of sample clusters, we simultaneously calibrate the mass-observable relation and constrain cosmological parameters. The calibrations using $sigma_v$ and Yx are consistent at the $0.6sigma$ level, with the $sigma_v$ calibration preferring ~16% higher masses. We use the full cluster dataset to measure $sigma_8(Omega_ m/0.27)^{0.3}=0.809pm0.036$. The SPT cluster abundance is lower than preferred by either the WMAP9 or Planck+WMAP9 polarization (WP) data, but assuming the sum of the neutrino masses is $sum m_ u=0.06$ eV, we find the datasets to be consistent at the 1.0$sigma$ level for WMAP9 and 1.5$sigma$ for Planck+WP. Allowing for larger $sum m_ u$ further reconciles the results. When we combine the cluster and Planck+WP datasets with BAO and SNIa, the preferred cluster masses are $1.9sigma$ higher than the Yx calibration and $0.8sigma$ higher than the $sigma_v$ calibration. Given the scale of these shifts (~44% and ~23% in mass, respectively), we execute a goodness of fit test; it reveals no tension, indicating that the best-fit model provides an adequate description of the data. Using the multi-probe dataset, we measure $Omega_ m=0.299pm0.009$ and $sigma_8=0.829pm0.011$. Within a $ u$CDM model we find $sum m_ u = 0.148pm0.081$ eV. We present a consistency test of the cosmic growth rate. Allowing both the growth index $gamma$ and the dark energy equation of state parameter $w$ to vary, we find $gamma=0.73pm0.28$ and $w=-1.007pm0.065$, demonstrating that the expansion and the growth histories are consistent with a LCDM model ($gamma=0.55; ,w=-1$).
