We present a power spectrum analysis of the final 2dF QSO Redshift Survey catalogue containing 22652 QSOs. Utilising the huge volume probed by the QSOs, we can accurately measure power out to scales of ~500Mpc 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 CMB 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 lambda 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 Gamma=0.13+-0.02. If an Einstein-de Sitter model r(z) is instead assumed, a slightly higher value of Gamma=0.16+-0.03 is obtained. A comparison with the Hubble Volume LCDM simulation shows very good agreement over the whole range of scales considered. A standard (Omega_m=1) CDM model, however, predicts a much higher value of Gamma 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 find that models with baryon oscillations are slightly preferred, with the baryon fraction Omega_b/Omega_m=0.18+-0.10. The overall shape of the power spectrum provides a strong constraint on Omega_m*h (where h is the Hubble parameter), with Omega_m*h=0.19+-0.05.
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