Constraints on shear and rotation with massive galaxy clusters

A precise determination of the mass function is an important tool to verify cosmological predictions of the Lambda 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 thematter density parameter Omega(m), the matter power spectrum normalization sigma(8) and the equation of state parameter wde of the dark energy fluid. In this work, using data on massive galaxy clusters (M > 8 x 10(14) h(-1)M(circle dot)) in the redshift range 0.05 < z < 0.83, for the first time we put constraints on the parameter a 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 s8 fixed and restricting our analysis to a Lambda CDM model, we find, at 1 sigma confidence level, Omega(m) = 0.284 similar to 0.0064, h = 0.678 similar to 0.017 and beta = 0.0019(-0.0015)(+0.0008,) where beta represents the slope of the parameter a. This result translates into a 9 per cent decrement of the number of massive clusters with respect to a standard Lambda CDM mass function, but better data are required to better constrain this quantity, since at the 2 sigma and 3 sigma confidence level we are only able to infer upper limits.