Cosmological parameters from SDSS and WMAP

We measure cosmological parameters using the three-dimensional power spectrum $P(k)$ from over 200 000 galaxies in the Sloan Digital Sky Survey (SDSS) in combination with Wilkinson Microwave Anisotropy Probe (WMAP) and other data. Our results are consistent with a ``vanilla'' flat adiabatic cold dark matter model with a cosmological constant without tilt ${(n}_{s}=1),$ running tilt, tensor modes, or massive neutrinos. Adding SDSS information more than halves the WMAP-only error bars on some parameters, tightening $1\ensuremath{\sigma}$ constraints on the Hubble parameter from $h\ensuremath{\approx}{0.74}_{\ensuremath{-}0.07}^{+0.18}$ to $h\ensuremath{\approx}{0.70}_{\ensuremath{-}0.03}^{+0.04},$ on the matter density from ${\ensuremath{\Omega}}_{m}\ensuremath{\approx}0.25\ifmmode\pm\else\textpm\fi{}0.10$ to ${\ensuremath{\Omega}}_{m}\ensuremath{\approx}0.30\ifmmode\pm\else\textpm\fi{}0.04$ $(1\ensuremath{\sigma})$ and on neutrino masses from $<11$ to $<0.6\mathrm{eV}$ (95%). SDSS helps even more when dropping prior assumptions about curvature, neutrinos, tensor modes and the equation of state. Our results are in substantial agreement with the joint analysis of WMAP and the Two Degree Field Galaxy Redshift Survey, which is an impressive consistency check with independent redshift survey data and analysis techniques. In this paper, we place particular emphasis on clarifying the physical origin of the constraints, i.e., what we do and do not know when using different data sets and prior assumptions. For instance, dropping the assumption that space is perfectly flat, the WMAP-only constraint on the measured age of the Universe tightens from ${t}_{0}\ensuremath{\approx}{16.3}_{\ensuremath{-}1.8}^{+2.3}\mathrm{Gyr}$ to ${t}_{0}\ensuremath{\approx}{14.1}_{\ensuremath{-}0.9}^{+1.0}\mathrm{Gyr}$ by adding SDSS and SN Ia data. Including tensors, running tilt, neutrino mass and equation of state in the list of free parameters, many constraints are still quite weak, but future cosmological measurements from SDSS and other sources should allow these to be substantially tightened.