  The redshift dependence of the abundance of galaxy clusters is very sensitive
to the statistical properties of primordial density perturbations. It can thus
be used to probe small deviations from Gaussian initial conditions. Such
deviations constitute a very important signature of many inflationary
scenarios, and are thus expected to provide crucial information on physical
processes which took place in the very early Universe.
  We have determined the biases which may be introduced in the estimation of
cosmological parameters by wrongly assuming the absence of primordial
non-Gaussianities. Although we find that the estimation of the present-day dark
energy density using cluster counts is not very sensitive to the non-Gaussian
properties of the density field, we show that the biases can be considerably
larger in the estimation of the dark energy equation of state parameter $w$ and
of the amplitude of the primordial density perturbations.
  Our results suggest that a significant level of non-Gaussianity at cluster
scales may be able to reconcile the constraint on the amplitude of the
primordial perturbations obtained using galaxy cluster number counts from the
Planck Sunyaev-Zeldovich Catalog with that obtained from the primary Cosmic
Microwave Background anisotropies measured by the Planck satellite.
