Fundamental Physics from Future Weak-Lensing Calibrated Sunyaev-Zel'dovich Galaxy Cluster Counts

Future high-resolution measurements of the cosmic microwave background (CMB) will produce catalogs of tens of thousands of galaxy clusters through the thermal Sunyaev-Zel'dovich (tSZ) effect. We forecast how well different configurations of a CMB Stage-4 experiment can constrain cosmological parameters, in particular the amplitude of structure as a function of redshift $\sigma_8(z)$, the sum of neutrino masses $\Sigma m_{\nu}$, and the dark energy equation of state $w(z)$. A key element of this effort is calibrating the tSZ scaling relation by measuring the lensing signal around clusters. We examine how the mass calibration from future optical surveys like the Large Synoptic Survey (LSST) compares with a purely internal calibration using lensing of the CMB itself. We find that, due to its high-redshift leverage, internal calibration gives constraints on cosmological parameters comparable to the optical calibration, and can be used as a cross-check of systematics in the optical measurement. We also show that in contrast to the constraints using the CMB lensing power spectrum, lensing-calibrated tSZ cluster counts can detect a minimal $\Sigma m_{\nu}$ at the 3-5$\sigma$ level even when the dark energy equation of state is freed up.