  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.

Astrophysics