Joint Cosmic Microwave Background and Weak Lensing Analysis: Constraints on Cosmological Parameters

We use cosmic microwave background (CMB) observations together with the red-sequence cluster survey weak lensing results to derive constraints on a range of cosmological parameters. This particular choice of observations is motivated by their robust physical interpretation and complementarity. Our combined analysis, including a weak nucleosynthesis constraint, yields accurate determinations of a number of parameters including the amplitude of fluctuations ${\sigma }_8=0.89\pm 0.05$ and matter density ${\Omega }_m=0.30\pm 0.03$. We also find a value for the Hubble parameter of $H_0=70\pm 3\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$, in good agreement with the Hubble Space Telescope key-project result. We conclude that the combination of CMB and weak lensing data provides some of the most powerful constraints available in cosmology today.

Figure 1

One-dimensional, marginalized probability distributions for a selection of parameters. The dashed curves are for CMB only. The solid curves include the RCS data. We see the weak lensing data, while being consistent with the CMB only results, narrow down a number of distributions considerably. In particular, the combination of data provides a tight independent constraint on $H_0$. The matter density and fluctuation amplitude are also much better constrained with the combination of CMB and weak lensing than with just CMB.

Figure 2

The two-dimensional, marginalized likelihoods for the $({\Omega }_m,{\sigma }_8)$ plane. The overlaid, filled contours show the 68% and 95% integration levels for the distributions. Bottom: RCS only; middle: CMB only; top: $\mathrm{C}\mathrm{M}\mathrm{B}+\mathrm{R}\mathrm{C}\mathrm{S}$.