Towards cosmological concordance on galactic scales

We use the observed abundance and clustering of galaxies from the 2dF Galaxy Redshift Survey to determine the matter density Omega(m) and the linear amplitude of mass fluctuations sigma(8). We use a method based on the conditional luminosity function, which allows straightforward computation of the luminosity-dependent bias, b, of galaxies with respect to the matter distribution. This allows us to break the degeneracy between bias and sigma(8), which has hampered previous attempts of using large-scale structure (LSS) data to determine sigma(8). In addition, it allows the inclusion of constraints on the redshift space distortion parameter beta=Omega(m)(0.6)/b, and yields average mass-to-light ratios as a function of halo mass. Using only the luminosity function and the correlation lengths as a function of luminosity we obtain constraints on Omega(m) and sigma(8) that are in good agreement with COBE. Models with low Omega(m) and high sigma(8) as well as those with high Omega(m) and low sigma(8) are ruled out because they over (under)predict the amount of clustering, respectively. We find the cluster mass-to-light ratio, <M-vir/L>(cl), to be strongly correlated with sigma(8). Using the additional constraints <M-vir/L>(cl)= (350 +/- 70) h (M/L)(circle dot) and beta= 0.49 +/- 0.09 as Gaussian priors significantly tightens the constraints and allows us to break the degeneracy between Omega(m) and sigma(8). For flat Lambda-cold dark matter (LambdaCDM) cosmologies with scale-invariant power spectra, we obtain that Omega(m)= 0.27(-0.10)(+0.14) and sigma(8)= 0.70 +/- 0.11 (both 95 per cent confidence limit). Adding constraints from current cosmic microwave background data, and extending the analysis to a larger cosmological parameter space, we obtain that Omega(m)= 0.24 +/- 0.07 and sigma(8)= 0.74(-0.10)(+0.13) (both 95 per cent confidence limit). Thus, we find clear evidence that both the matter density Omega(m) and the mass variance sigma(8) are significantly lower than their 'standard' concordance values of 0.3 and 0.9, respectively. We show that cosmologies with Omega(m)similar or equal to 0.25 and sigma(8)similar or equal to 0.75, as favoured here, predict dark matter haloes that are significantly less centrally concentrated than for the standard LambdaCDM concordance cosmology. We argue that this may solve both the problem with the rotation curves of dwarf and low surface brightness galaxies, as well as the problem of simultaneously matching the galaxy luminosity function and the Tully-Fisher zero-point.