We create a sample of spectroscopically identified galaxies with z < 0.2 from the Sloan Digital Sky Survey (SDSS) Data Release 7, covering 6813 deg 2 . Galaxies are chosen to sample the highest mass haloes, with an effective bias of 1.5, allowing us to construct 1000 mock galaxy catalogs (described in Paper II), which we use to estimate statistical errors and test our methods. We use an estimate of the gravitational potential to "reconstruct" the linear density fluctuations, enhancing the Baryon Acoustic Oscillation (BAO) signal in the measured correlation function and power spectrum. Fitting to these measurements, we determine D V (z eff = 0.15) = (664 ± 25)(r d /r d,fid ) Mpc; this is a better than 4 per cent distance measurement. This "fills the gap" in BAO distance ladder between previously measured local and higher redshift measurements, and affords significant improvement in constraining the properties of dark energy. Combining our measurement with other BAO measurements from BOSS and 6dFGS galaxy samples provides a 15 per cent improvement in the determination of the equation of state of dark energy and the value of the Hubble parameter at z = 0 (H 0 ). Our measurement is fully consistent with the Planck results and the ΛCDM concordance cosmology, but increases the tension between Planck+BAO H 0 determinations and direct H 0 measurements.

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We derive constraints on cosmological parameters and tests of dark energy models from the combination of baryon acoustic oscillation (BAO) measurements with cosmic microwave background (CMB) data and a recent reanalysis of Type Ia supernova (SN) data. In particular, we take advantage of high-precision BAO measurements from galaxy clustering and the Lyman-α forest (LyaF) in the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS). Treating the BAO scale as an uncalibrated standard ruler, BAO data alone yield a high confidence detection of dark energy; in combination with the CMB angular acoustic scale they further imply a nearly flat universe. Adding the CMB-calibrated physical scale of the sound horizon, the combination of BAO and SN data into an "inverse distance ladder" yields a measurement of H0 = 67.3 ± 1.1 km s −1 Mpc −1 , with 1.7% precision. This measurement assumes standard pre-recombination physics but is insensitive to assumptions about dark energy or space curvature, so agreement with CMB-based estimates that assume a flat ΛCDM cosmology is an important corroboration of this minimal cosmological model. For constant dark energy (Λ), our BAO+SN+CMB combination yields matter density Ωm = 0.301 ± 0.008 and curvature Ω k = −0.003 ± 0.003. When we allow more general forms of evolving dark energy, the BAO+SN+CMB parameter constraints are always consistent with flat ΛCDM values at ≈ 1σ. While the overall χ 2 of model fits is satisfactory, the LyaF BAO measurements are in moderate (2 − 2.5σ) tension with model predictions. Models with early dark energy that tracks the dominant energy component at high redshift remain consistent with our expansion history constraints, and they yield a higher H0 and lower matter clustering amplitude, improving agreement with some low redshift observations. Expansion history alone yields an upper limit on the summed mass of neutrino species, mν < 0.56 eV (95% confidence), improving to mν < 0.25 eV if we include the lensing signal in the Planck CMB power spectrum. In a flat ΛCDM model that allows extra relativistic species, our data combination yields N eff = 3.43 ± 0.26; while the LyaF BAO data prefer higher N eff when excluding galaxy BAO, the galaxy BAO alone favor N eff ≈ 3. When structure growth is extrapolated forward from the CMB to low redshift, standard dark energy models constrained by our data predict a level of matter clustering that is high compared to most, but not all, observational estimates.

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Cosmological parameter constraints from the CMB power spectra alone suffer several well-known degeneracies. These degeneracies can be broken by numerical artefacts and also a variety of physical effects that become quantitatively important with high-accuracy data e.g. from the Planck satellite. We study degeneracies in models with flat and non-flat spatial sections, non-trivial dark energy and massive neutrinos, and investigate the importance of various physical degeneracy-breaking effects. We test the camb power spectrum code for numerical accuracy, and demonstrate that the numerical calculations are accurate enough for degeneracies to be broken mainly by true physical effects (the integrated Sachs-Wolfe effect, CMB lensing and geometrical and other effects through recombination) rather than numerical artefacts. We quantify the impact of CMB lensing on the power spectra, which inevitably provides degeneracy-breaking information even without using information in the non-Gaussianity. Finally we check the numerical accuracy of sample-based parameter constraints using camb and CosmoMC. In an appendix we document recent changes to camb's numerical treatment of massive neutrino perturbations, which are tested along with other recent improvements by our degeneracy exploration results.