The 2dF QSO Redshift Survey - VII. Constraining Cosmology from Redshift Space Distortions via xi(sigma,pi)

We describe a method from which cosmology may be constrained from the 2QZ Survey. By comparing clustering properties parallel and perpendicular to the line of sight and by modeling the effects of redshift space distortions, we are able to study geometric distortions in the clustering pattern which occur if a wrong cosmology is assumed when translating redshifts into comoving distances. Using mock 2QZ catalogues, drawn from the Hubble Volume simulation, we find, that there is a degeneracy between the geometric and the redshift-space distortions that makes it difficult to obtain an unambiguous estimate of Omega_{m}(0) from the geometric tests alone. However, we demonstrate a new method to determine the cosmology which works by combining the above geometric test with a test based on the evolution of the QSO clustering amplitude. We find that we are able to break the degeneracy and that independent constraints to +-20% (1 sigma) accuracy on Omega_{m}(0) and +-10% (1 sigma) accuracy on beta_{QSO}(z) should be possible in the full 2QZ survey. Finally we apply the method to the 10k catalogue of 2QZ QSOs. The smaller number of QSOs and the current status of the Survey mean that a strong result on cosmology is not possible but we do constrain beta_{QSO}(z) to 0.35+-0.2. By combining this constraint with the further constraint available from the amplitude of QSO clustering, we find tentative evidence favouring a model with non-zero Omega_{Lambda}(0), although an Omega_{m}(0)=1 model provides only a marginally less good fit. A model with Omega_{Lambda}(0)=1 is ruled out. The results are in agreement with those found by Outram et al. using a similar analysis in Fourier space. (Abridged)