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 function of halo mass .
Using only the luminosity function and the correlation lengths as 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 , \langle M _ { vir } / L \rangle _ { cl } , to be strongly correlated with \sigma _ { 8 } .
Using the additional constraints \langle M _ { vir } / L \rangle _ { cl } = ( 350 \pm 70 ) h\ > ( { M } / { L } ) _ { \odot } and \beta = 0.49 \pm 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 CDM cosmologies with scale-invariant power spectra we obtain that \Omega _ { m } = 0.27 ^ { +0.14 } _ { -0.10 } and \sigma _ { 8 } = 0.77 ^ { +0.10 } _ { -0.14 } ( both 95 % CL ) .
Adding constraints from current CMB data , and extending the analysis to a larger cosmological parameter space , we obtain that \Omega _ { m } = 0.25 ^ { +0.10 } _ { -0.07 } and \sigma _ { 8 } = 0.78 \pm 0.12 ( both 95 % CL ) .
Thus , we find strong indications 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 } \simeq 0.25 and \sigma _ { 8 } \simeq 0.75 , as favored here , predict dark matter haloes that are significantly less centrally concentrated than for the standard \Lambda CDM 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 .