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

Biased cosmological parameter estimation with galaxy cluster counts in the presence of primordial non-Gaussianities