Cosmological parameter analysis including SDSS Ly-alpha forest and galaxy bias: constraints on the primordial spectrum of fluctuations, neutrino mass, and dark energy

We combine the constraints from the recent Ly-alpha forest and bias analysis of the SDSS with previous constraints from SDSS galaxy clustering, the latest supernovae, and WMAP . Combining WMAP and the lya we find for the primordial slope n_s=0.98\pm 0.02. We see no evidence of running, dn/d\ln k=-0.003\pm 0.010, a factor of 3 improvement over previous constraints. We also find no evidence of tensors, r<0.36 (95% c.l.). A positive correlation between tensors and primordial slope disfavors chaotic inflation type models with steep slopes: V \propto φ^4 is outside the 3-sigma contour. For the amplitude we find sigma_8=0.90\pm 0.03 from the lyaf and WMAP alone. We find no evidence of neutrino mass: for the case of 3 massive neutrino families with an inflationary prior, \sum m_ν<0.42eV and the mass of lightest neutrino is m_1<0.13eV at 95% c.l. For the 3 massless + 1 massive neutrino case we find m_ν<0.79eV for the massive neutrino, excluding at 95% c.l. all neutrino mass solutions compatible with the LSND results. We explore dark energy constraints in models with a fairly general time dependence of dark energy equation of state, finding Omega_lambda=0.72\pm 0.02, w(z=0.3)=-0.98^{+0.10}_{-0.12}, the latter changing to w(z=0.3)=-0.92^{+0.09}_{-0.10} if tensors are allowed. We find no evidence for variation of the equation of state with redshift, w(z=1)=-1.03^{+0.21}_{-0.28}. These results rely on the current understanding of the lyaf and other probes, which need to be explored further both observationally and theoretically, but extensive tests reveal no evidence of inconsistency among different data sets used here.