  We combine the Ly-alpha forest power spectrum (LYA) from the Sloan Digital
Sky Survey (SDSS) and high resolution spectra with cosmic microwave background
(CMB) including 3-year WMAP, and supernovae (SN) and galaxy clustering
constraints to derive new constraints on cosmological parameters. The existing
LYA power spectrum analysis is supplemented by constraints on the mean flux
decrement derived using a principle component analysis for quasar continua,
which improves the LYA constraints on the linear power. We find some tension
between the WMAP3 and LYA power spectrum amplitudes, at the ~2 sigma level,
which is partially alleviated by the inclusion of other observations: we find
\sigma_8=0.85\pm 0.02 compared to sigma_8=0.80 \pm 0.03 without LYA. For the
slope we find ns=0.965\pm0.012. We find no evidence for the running of the
spectral index in the combined analysis, dn/dln k=-(1.5\pm 1.2) x 10^{-2}, in
agreement with inflation. The limits on the sum of neutrino masses are
significantly improved: $\sum m_{\nu}<0.17\eV$ at 95% (<0.32eV at 99.9%). This
result, when combined with atmospheric and solar neutrino mixing constraints,
requires that the neutrino masses cannot be degenerate, m_3/m_1>1.3 (95% c.l.).
Assuming a thermalized fourth neutrino we find m_s<0.26\eV at 95% c.l. and such
neutrino cannot be an explanation for the LSND results. In the limits of
massless neutrinos we obtain the effective number of neutrinos N_\nu^{\rm
eff}=5.3^{+0.4}_{-0.6}{}^{+2.1}_{-1.7}{}^{+3.8}_{-2.5} and N_\nu^{\rm eff}=3.04
is allowed only at 2.4-sigma. The constraint on the dark energy equation of
state is w=-1.04\pm 0.06. The constraint on curvature is Omega_k=-0.003\pm
0.006. Cosmic strings limits are G\mu <2.3 x 10^{-7} at 95% c.l. and correlated
isocurvature models are also tightly constrained.
