Cosmological parameter analysis including SDSS Ly<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>forest and galaxy bias: Constraints on the primordial spectrum of fluctuations, neutrino mass, and dark energy

We combine the constraints from the recent Ly$\ensuremath{\alpha}$ forest analysis of the Sloan Digital Sky Survey (SDSS) and the SDSS galaxy bias analysis with previous constraints from SDSS galaxy clustering, the latest supernovae, and 1st year WMAP cosmic microwave background anisotropies. We find significant improvements on all of the cosmological parameters compared to previous constraints, which highlights the importance of combining Ly$\ensuremath{\alpha}$ forest constraints with other probes. Combining WMAP and the Ly$\ensuremath{\alpha}$ forest we find for the primordial slope ${n}_{s}=0.98\ifmmode\pm\else\textpm\fi{}0.02$. We see no evidence of running, $dn/d\mathrm{ln}k=\ensuremath{-}0.003\ifmmode\pm\else\textpm\fi{}0.010$, a factor of $3$ improvement over previous constraints. We also find no evidence of tensors, $r&lt;0.36$ ($95%$ c.l.). Inflationary models predict the absence of running and many among them satisfy these constraints, particularly negative curvature models such as those based on spontaneous symmetry breaking. A positive correlation between tensors and primordial slope disfavors chaotic inflation-type models with steep slopes: while the $V\ensuremath{\propto}{\ensuremath{\phi}}^{2}$ model is within the 2-sigma contour, $V\ensuremath{\propto}{\ensuremath{\phi}}^{4}$ is outside the 3-sigma contour. For the amplitude we find ${\ensuremath{\sigma}}_{8}=0.90\ifmmode\pm\else\textpm\fi{}0.03$ from the Ly$\ensuremath{\alpha}$ forest and WMAP alone. We find no evidence of neutrino mass: for the case of $3$ massive neutrino families with an inflationary prior, $\ensuremath{\sum}_{}^{}{m}_{\ensuremath{\nu}}&lt;0.42$ eV and the mass of lightest neutrino is ${m}_{1}&lt;0.13$ eV at $95%$ c.l. For the 3 massless $+1$ massive neutrino case we find ${m}_{\ensuremath{\nu}}&lt;0.79$ eV 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 ${\ensuremath{\Omega}}_{\ensuremath{\lambda}}=0.72\ifmmode\pm\else\textpm\fi{}0.02$, $\mathrm{w}(z=0.3)=\ensuremath{-}{0.98}_{\ensuremath{-}0.12}^{+0.10}$, the latter changing to $\mathrm{w}(z=0.3)=\ensuremath{-}{0.92}_{\ensuremath{-}0.10}^{+0.09}$ if tensors are allowed. We find no evidence for variation of the equation of state with redshift, $\mathrm{w}(z=1)=\ensuremath{-}{1.03}_{\ensuremath{-}0.28}^{+0.21}$. These results rely on the current understanding of the Ly$\ensuremath{\alpha}$ forest 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.