Power spectrum normalization and the non-Gaussian halo model

The normalization of the matter power spectrum, sigma(8), is an essential ingredient to predict the phenomenology of the low-redshift Universe. It has been measured using several methods, such as X-ray cluster counts, weak lensing and the cosmic microwave background (CMB), which have yielded values ranging from 0.7 to 1.0. While these differences could be due to systematic effects, they could also be due to physics beyond the standard Lambda cold dark matter (ACDM) model. An obvious possibility is the presence of non-Gaussian initial fluctuations in the density field. To study the impact of non-Gaussianity on each of these methods, we use a generalized halo model to compute cluster counts and the non-linear power spectrum for non-Gaussian models. For the quadratic coupling model, the upper limits on non-Gaussianity from the WMAP CMB experiment correspond to roughly a 4 per cent shift in sigma(8) as measured from cluster counts and about 2 per cent shift through weak lensing. This is not enough to account for the cut-rent internal and mutual discrepancies between the different methods, unless the scale dependence of non-Gaussianity is stronger than that for quadratic coupling. A comparison between future X-ray surveys with a two-fold improvement in cluster mass calibration and future cosmic shear surveys with 400 deg(2) will be required to constrain non-Gaussianity on small scales with a precision matching that of the current CMB constraints on larger scales. Our results argue for the presence of systematics in the current cluster and cosmic shear surveys, or to non-standard physics other than non-Gaussianity.