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 Ω m and the linear amplitude of mass fluctuations σ 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 σ 8 , which has hampered previous attempts of using large‐scale structure (LSS) data to determine σ 8 . In addition, it allows the inclusion of constraints on the redshift space distortion parameter β=Ω 0.6 m / 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 Ω m and σ 8 that are in good agreement with COBE . Models with low Ω m and high σ 8 as well as those with high Ω m and low σ 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 σ 8 . Using the additional constraints 〈 M vir / L 〉 cl = (350 ± 70) h (M/L) ⊙ and β= 0.49 ± 0.09 as Gaussian priors significantly tightens the constraints and allows us to break the degeneracy between Ω m and σ 8 . For flat Λ‐cold dark matter (ΛCDM) cosmologies with scale‐invariant power spectra, we obtain that Ω m = 0.27 +0.14 −0.10 and σ 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 Ω m = 0.24 ± 0.07 and σ 8 = 0.74 +0.13 −0.10 (both 95 per cent confidence limit). Thus, we find clear evidence that both the matter density Ω m and the mass variance σ 8 are significantly lower than their ‘standard’ concordance values of 0.3 and 0.9, respectively. We show that cosmologies with Ω m ≃ 0.25 and σ 8 ≃ 0.75 , as favoured here, predict dark matter haloes that are significantly less centrally concentrated than for the standard ΛCDM 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.