| Abstract
| - Abstract. We use the observed abundance and clustering of galaxies from the 2dF Galaxy Redshift Survey to determine the matter density Ωm and the linear amplitude of mass fluctuations σ8. 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 σ8, which has hampered previous attempts of using large-scale structure (LSS) data to determine σ8. In addition, it allows the inclusion of constraints on the redshift space distortion parameter β=Ω0.6m/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 Ωm and σ8 that are in good agreement with COBE. Models with low Ωm and high σ8 as well as those with high Ωm and low σ8 are ruled out because they over (under)predict the amount of clustering, respectively. We find the cluster mass-to-light ratio, 〈Mvir/L〉cl, to be strongly correlated with σ8. Using the additional constraints 〈Mvir/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 Ωm and σ8. For flat Λ-cold dark matter (ΛCDM) cosmologies with scale-invariant power spectra, we obtain that Ωm= 0.27+0.14−0.10 and σ8= 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 Ωm= 0.24 ± 0.07 and σ8= 0.74+0.13−0.10 (both 95 per cent confidence limit). Thus, we find clear evidence that both the matter density Ωm and the mass variance σ8 are significantly lower than their ‘standard’ concordance values of 0.3 and 0.9, respectively. We show that cosmologies with Ωm≃ 0.25 and σ8≃ 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.
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