A precise determination of the mass function is an important tool to verify cosmological predictions of the cold dark matter (CDM) model and to infer more precisely the better model describing the evolution of the Universe. Galaxy clusters have been currently used to infer cosmological parameters, in particular the matter density parameter m , the matter power spectrum normalization σ 8 and the equation of state parameter wde of the dark energy fluid. In this work, using data on massive galaxy clusters (M > 8 × 1014 h−1 M) in the redshift range 0.05 z 0.83, for the first time we put constraints on the parameter α introduced within the formalism of the extended spherical collapse model to quantify deviations from sphericity due to shear and rotation. Since at the moment there is no physical model describing its functional shape, we assume it to be a logarithmic function of the cluster mass. By holding σ 8 fixed and restricting our analysis to a CDM model, we find, at 1σ confidence level, m = 0.284 ± 0.0064, h = 0.678 ± 0.017 and β = 0.0019−0.0015 +0.0008 , where β represents the slope of the parameter α. This result translates into a 9 per cent decrement of the number of massive clusters with respect to a standard CDM mass function, but better data are required to better constrain this quantity, since at the 2σ and 3σ confidence level we are only able to infer upper limits.
