Probing Cosmology and Galaxy Cluster Structure with the
  Sunyaev-Zel'dovich Decrement vs. X-ray Temperature Scaling Relation
  Scaling relations among galaxy cluster observables, which will become
available in large future samples of galaxy clusters, could be used to
constrain not only cluster structure, but also cosmology. We study the utility
of this approach, employing a physically motivated parametric model to describe
cluster structure, and applying it to the expected relation between the
Sunyaev-Zel'dovich decrement (S_\nu) and the emission-weighted X-ray
temperature (T_ew). The slope and normalization of the entropy profile, the
concentration of the dark matter potential, the pressure at the virial radius,
and the level of non-thermal pressure support, as well as the mass and
redshift-dependence of these quantities are described by free parameters. With
a suitable choice of fiducial parameter values, the cluster model satisfies
several existing observational constraints. We employ a Fisher matrix approach
to estimate the joint errors on cosmological and cluster structure parameters
from a measurement of S_\nu vs. T_ew in a future survey. We find that different
cosmological parameters affect the scaling relation differently: predominantly
through the baryon fraction (\Omega_m and \Omega_b), the virial overdensity
(w_0 and w_a for low-z clusters) and the angular diameter distance (w_0, w_a
for high-z clusters; \Omega_DE and h). We find that the cosmology constraints
from the scaling relation are comparable to those expected from the number
counts (dN/dz) of the same clusters. The scaling relation approach is
relatively insensitive to selection effects and it offers a valuable
consistency check; combining the information from the scaling relation and
dN/dz is also useful to break parameter degeneracies and help disentangle
cluster physics from cosmology.
