The 2dF QSO Redshift Survey - XI. The QSO power spectrum

We present a power spectrum analysis of the final 2dF Quasi-Stellar Object (QSO) Redshift Survey catalogue containing 22 652 QSOs. Utilizing the huge volume probed by the QSOs, we can accurately measure power out to scales of ~500 h^-1 Mpc and derive new constraints, at z~ 1.4, on the matter and baryonic contents of the Universe. Importantly, these new cosmological constraints are derived at an intermediate epoch between the cosmic microwave background observations at z~ 1000, and local (z~ 0) studies of large-scale structure; the average QSO redshift corresponds to a look-back time of approximately two-thirds of the age of the Universe. We find that the amplitude of clustering of the QSOs at z~ 1.4 is similar to that of present-day galaxies. The power spectra of the QSOs at high and low redshift are compared and we find little evidence for any evolution in the amplitude. Assuming a Λ cosmology to derive the comoving distances, r(z), to the QSOs, the power spectrum derived can be well described by a model with shape parameter Γ= 0.13 +/- 0.02. If an Einstein-de Sitter model r(z) is instead assumed, a slightly higher value of Γ= 0.16 +/- 0.03 is obtained. A comparison with the Hubble Volume Λ cold dark matter (CDM) simulation shows very good agreement over the whole range of scales considered. A standard (Ω_m= 1) CDM model, however, predicts a much higher value of Γ than is observed, and it is difficult to reconcile such a model with these data. We fit CDM model power spectra (assuming scale-invariant initial fluctuations), convolved with the survey window function, and corrected for redshift space distortions, and we find that models with baryon oscillations are slightly preferred, with the baryon fraction Ω_b/Ω_m= 0.18 +/- 0.10. The overall shape of the power spectrum provides a strong constraint on Ω_mh (where h is the Hubble parameter), with Ω_mh= 0.19 +/- 0.05.