The 2dF QSO Redshift Survey - VII. Constraining cosmology from redshift-space distortions via ξ (σ , π )

We describe a method from which cosmology may be constrained from the 2dF QSO Redshift Survey (2QZ). By comparing clustering properties parallel and perpendicular to the line of sight and by modelling 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. Alcock & Paczyński pointed out that this technique was particularly sensitive as a test for a large cosmological constant, Λ. Using mock 2QZ catalogues, drawn from the Hubble Volume simulation, we find that there is a degeneracy between the geometric distortions and the redshift-space distortions, parametrized by β _QSO (z ), that makes it difficult to obtain an unambiguous estimate of Ω_m (0), the matter density parameter, from the geometric tests alone. This is in agreement with the conclusions of Ballinger et al. However, we demonstrate that by combining results from the above geometric test with those from a second test based on the evolution of the QSO clustering amplitude, which has a different dependence on β _QSO (z ) and Ω_m (0), we are able to place stronger constraints on cosmology. In the analysis of the Hubble Volume mock catalogues we find that we are able to break the degeneracy between Ω_m (0) and β _QSO (z ) and that independent constraints to +/-20 per cent (1σ ) accuracy on Ω_m (0) and +/-10 per cent (1σ ) accuracy on β _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 β _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 Ω_Λ (0), although an Ω_m (0)=1 model provides only a marginally less good fit. A model with Ω_Λ (0)=1 is ruled out. The results are in agreement with those found by Outram et al. using a similar analysis in Fourier space.