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 $\Lambda$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 $\Omega_{\rm m}$, the matter power spectrum normalization
$\sigma_8$ and the equation of state parameter $w_{\rm de}$ of the dark energy
fluid. In this work, using data on massive galaxy clusters ($M>8\times
10^{14}~h^{-1}~M_{\odot}$) in the redshift range $0.05\lesssim z\lesssim 0.83$
we put constraints on the parameter $\alpha$ 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 $\sigma_8$ fixed and restricting our analysis to a
$\Lambda$CDM model, we find, at $1-\sigma$ confidence level, $\Omega_{\rm
m}=0.284\pm0.0064$, $h=0.678\pm0.017$ and $\beta=0.0019^{+0.0008}_{-0.0015}$,
where $\beta$ represents the slope of the parameter $\alpha$. This results
translates into a $9\%$ 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.
