Density of cold dark matter

The nature of dark matter is increasingly constrained by cosmological data. In this paper, we examine the implications of the Cosmic Microwave Background anisotropy limits on the density of cold dark matter under different theoretical assumptions and combinations of datasets. We infer the constraint $\Omega_{cdm}h^2=0.12\pm0.04$ (at 95% c.l.). The CDM models are compared with the shape of the linear matter power spectrum inferred from the 2dF galaxy redshift survey and with the rms mass fluctuations from recent local cluster observations. We found that a value of $\sigma_8 \sim 1$ as suggested by recent cosmic shear data is not favoured by the CMB data alone nor by combined CMB+SN-Ia, CMB+HST or CMB+2dFGRS analyses. We also extrapolate our bounds on the rms linear mass fluctuations to sub-galactic scales and compare them with recent lensing constraints, finding agreement with the standard $\Lambda$CDM model.