  Sensitive surveys of the Cosmic Microwave Background will detect thousands of
galaxy clusters via the Sunyaev-Zel'dovich (SZ) effect. Two SZ observables, the
central or maximum and integrated Comptonization parameters y_max and Y, relate
in a simple way to the total cluster mass, which allow the construction of mass
functions (MFs) that can be used to estimate cosmological parameters such as
Omega_M, sigma_8, and the dark energy parameter w. However, clusters form from
the mergers of smaller structures, events that can disrupt the equilibrium of
intracluster gas upon which SZ-M relations rely. From a set of
N-body/hydrodynamical simulations of binary cluster mergers, we calculate the
evolution of Y and y_max over the course of merger events and find that both
parameters are transiently "boosted," primarily during the first core passage.
We then use a semi-analytic technique developed by Randall et al. (2002) to
estimate the effect of merger boosts on the distribution functions YF and yF of
Y and y_max, respectively, via cluster merger histories determined from
extended Press-Schechter (PS) merger trees. We find that boosts do not induce
an overall systematic effect on YFs, and the values of Omega_M, sigma_8, and w
were returned to within 2% of values expected from the nonboosted YFs. The
boosted yFs are significantly biased, however, causing Omega_M to be
underestimated by 15-45%, sigma_8 to be overestimated by 10-25%, and w to be
pushed to more negative values by 25-45%. We confirm that the integrated SZ
effect, Y, is far more robust to mergers than y_max, as previously reported by
Motl et al. (2005) and similarly found for the X-ray equivalent Y_X, and we
conclude that Y is the superior choice for constraining cosmological
parameters.
