The influence of mergers on the cluster temperature function and
  cosmological parameters derived from it
  We develop a parameter-free analytic model to include the effects of mergers
into the theoretical modelling of the X-ray temperature function of galaxy
clusters. We include this description into our model for the cluster population
based on fluctuations of the gravitational potential, which avoids any
reference to mass. Comparisons with a numerical simulation reveal that the
theoretical model is in good agreement with the simulation results. We show
that building the model on the dynamics of spherical rather than ellipsoidal
collapse yields better results if emission-weighted temperatures are used,
while ellipsoidal collapse yields good agreement between model and simulation
for mass-weighted temperatures. Analysing two different samples of X-ray
clusters, we quantify the influence of mergers and a conversion between
different temperature definitions on the joint determination of Omega_m0 and
sigma_8. If effects of mergers are included, temperature functions based on
cluster masses and on the gravitational potential built on spherical collapse
are in good agreement with other cosmological probes without any conversion of
temperatures.
