We report on measurements of the cosmological constant, Lambda, and the redshift space distortion parameter beta=Omega_m^0.6/b, based on an analysis of the QSO power spectrum parallel and perpendicular to the observers line of sight, from the final catalogue of the 2dF QSO Redshift Survey. We derive a joint Lambda - beta constraint from the geometric and redshift-space distortions in the power spectrum. By combining this result with a second constraint based on mass clustering evolution, we break this degeneracy and obtain strong constraints on both parameters. Assuming a flat cosmology and a Lambda cosmology r(z) function to convert from redshift into comoving distance, we find best fit values of Omega_Lambda=0.71^{+0.09}_{-0.17} and beta(z~1.4)=0.45^{+0.09}_{-0.11}. Assuming instead an EdS cosmology r(z) we find that the best fit model obtained, with Omega_Lambda=0.64^{+0.11}_{-0.16} and beta(z~1.4)=0.40^{+0.09}_{-0.09}, is consistent with the Lambda r(z) results, and inconsistent with a Lambda=0 flat cosmology at over 95 per cent confidence.
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