Parameter constraints for flat cosmologies from cosmic microwave background and 2dFGRS power spectra

We constrain flat cosmological models with a joint likelihood analysis of a new compilation of data from the cosmic microwave background (CMB) and from the 2dF Galaxy Redshift Survey (2dFGRS). Fitting the CMB alone yields a known degeneracy between the Hubble constant h and the matter density Ωm, which arises mainly from preserving the location of the peaks in the angular power spectrum. This 'horizon-angle degeneracy' is considered in some detail and is shown to follow the simple relation Ωm h3.4 = constant. Adding the 2dF-GRS power spectrum constrains Ωm h and breaks the degeneracy. If tensor anisotropies are assumed to be negligible, we obtain values for the Hubble constant of h = 0.665±0.047, the matter density Ωm = 0.313±0.055, and the physical cold dark matter and baryon densities Ωm h2 = 0.115±0.009, Ωm h2 = 0.022±0.002 (standard rms errors). Including a possible tensor component causes very little change to these figures; we set an upper limit to the tensor-to-scalar ratio of r < 0.7 at a 95 per cent confidence level. We then show how these data can be used to constrain the equation of state of the vacuum, and find w < -0.52 at 95 per cent confidence. The preferred cosmological model is thus very well specified, and we discuss the precision with which future CMB data can be predicted, given the model assumptions