The 2dF QSO Redshift Survey - VI. Measuring Λ and β from redshift-space distortions in the power spectrum

When the 2dF QSO Redshift Survey (2QZ) is complete, a powerful geometric test for the cosmological constant will be available. By comparing the clustering along and across the line of sight and modelling the effects of peculiar velocities and bulk motions in redshift space, geometric distortions, which occur if the wrong cosmology is assumed, can be detected. In this paper we investigate the effect of geometric and redshift-space distortions in the power spectrum parallel and perpendicular to the observer's line of sight, [formmu2]P^S(k_∥,k_⊥). Ballinger et al. developed a model to estimate the cosmological constant, Λ, and the important parameter [formmu3]β~Ωm0.6/b from these distortions. We apply this model to a detailed simulation of the final 25k 2QZ, produced using the Virgo Consortium's huge Hubble Volume N-body ΛCDM (cold dark matter) light-cone simulation. We confirm the conclusions of Ballinger et al.: the shapes of the redshift-space and geometric distortions are very similar, and discriminating between the two to produce a purely geometric constraint on Λ is difficult. When all the uncertainties in measuring [formmu4]P^S(k_∥,k_⊥) for the 2QZ are taken into account, we find that only a joint [formmu5]Λ-β constraint is possible. By combining this result with a second constraint based on mass clustering evolution, however, we can make significant progress. We predict that this method should allow us to constrain β to approximately +/-0.1, and Ω_m to +/-0.25, using the final catalogue. We apply the method to the 2QZ catalogue of 10000 quasars (QSOs) and find that this incomplete catalogue marginally favours a Λ cosmology, obtaining best-fitting values of [formmu6]β=0.39-0.17+0.18 and [formmu7]Ω_m=1-Ω_Λ=0.23- 0.13+0.44. However, Einstein-de Sitter [formmu8](Ω_m=1.0, [formmu9]Ω_Λ=0.0) models are only rejected at the 1.4σ level in the current survey. The rejection of lambda-dominated [formmu10](Ω_m=0.0, [formmu11]Ω_Λ=1.0) models is stronger at ~2σ.