Parameter constraints for flat cosmologies from CMB 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 ‘horizonangle degeneracy’ is considered in some detail and shown to follow a simple relation Ωmh 3.4 = constant. Adding the 2dFGRS power spectrum constrains Ωmh and breaks the degeneracy. If tensor anisotropies are assumed to be negligible, we obtain values for the Hubble constant h = 0.665±0.047, the matter density Ωm = 0.313±0.055, and the physical CDM and baryon densities Ωch 2 = 0.115 ± 0.009,Ωbh 2 = 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 95% confidence. 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% 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. The 2dFGRS power-spectrum data and covariance matrix, and the CMB data compilation used here, are available from http://www.roe.ac.uk/~wjp/. keywords: large-scale structure of Universe, cosmic microwave background, cosmological parameters