Cosmological Constraints from Moments of the Thermal Sunyaev-Zel'dovich
  Effect
  In this paper, we explain how moments of the thermal Sunyaev-Zel'dovich (tSZ)
effect can constrain both cosmological parameters and the astrophysics of the
intracluster medium (ICM). As the tSZ signal is strongly non-Gaussian, higher
moments of tSZ maps contain useful information. We first calculate the
dependence of the tSZ moments on cosmological parameters, finding that higher
moments scale more steeply with sigma_8 and are sourced by more massive galaxy
clusters. Taking advantage of the different dependence of the variance and
skewness on cosmological and astrophysical parameters, we construct a
statistic, |<T^3>|/<T^2>^1.4, which cancels much of the dependence on cosmology
(i.e., sigma_8) yet remains sensitive to the astrophysics of intracluster gas
(in particular, to the gas fraction in low-mass clusters). Constraining the ICM
astrophysics using this statistic could break the well-known degeneracy between
cosmology and gas physics in tSZ measurements, allowing for tight constraints
on cosmological parameters. Although detailed simulations will be needed to
fully characterize the accuracy of this technique, we provide a first
application to data from the Atacama Cosmology Telescope and the South Pole
Telescope. We estimate that a Planck-like full-sky tSZ map could achieve a <1%
constraint on sigma_8 and a 1-sigma error on the sum of the neutrino masses
that is comparable to the existing lower bound from oscillation measurements.
