Graziano Rossi

We present cosmological results from the final galaxy clustering data set of the Baryon Oscillation Spectroscopic Survey, part of the Sloan Digital Sky Survey III. Our combined galaxy sample comprises 1.2 million massive galaxies over an effective area of 9329 deg 2 and volume of 18.7 Gpc 3 , divided into three partially overlapping redshift slices centred at effective redshifts 0.38, 0.51 and 0.61. We measure the angular diameter distance D M and Hubble parameter H from the baryon acoustic oscillation (BAO) method, in combination with a cosmic microwave background prior on the sound horizon scale, after applying reconstruction to reduce non-linear effects on the BAO feature. Using the anisotropic clustering of the

We present the cosmological implications from final measurements of clustering using galaxies, quasars, and $\mathrm{Ly}\ensuremath{\alpha}$ forests from the completed Sloan Digital Sky Survey (SDSS) lineage of experiments in large-scale structure. These experiments, composed of data from SDSS, SDSS-II, BOSS, and eBOSS, offer independent measurements of baryon acoustic oscillation (BAO) measurements of angular-diameter distances and Hubble distances relative to the sound horizon, ${r}_{d}$, from eight different samples and six measurements of the growth rate parameter, $f{\ensuremath{\sigma}}_{8}$, from redshift-space distortions (RSD). This composite sample is the most constraining of its kind and allows us to perform a comprehensive assessment of the cosmological model after two decades of dedicated spectroscopic observation. We show that the BAO data alone are able to rule out dark-energy-free models at more than eight standard deviations in an extension to the flat, $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model that allows for curvature. When combined with Planck Cosmic Microwave Background (CMB) measurements of temperature and polarization, under the same model, the BAO data provide nearly an order of magnitude improvement on curvature constraints relative to primary CMB constraints alone. Independent of distance measurements, the SDSS RSD data complement weak lensing measurements from the Dark Energy Survey (DES) in demonstrating a preference for a flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmological model when combined with Planck measurements. The combined BAO and RSD measurements indicate ${\ensuremath{\sigma}}_{8}=0.85\ifmmode\pm\else\textpm\fi{}0.03$, implying a growth rate that is consistent with predictions from Planck temperature and polarization data and with General Relativity. When combining the results of SDSS BAO and RSD, Planck, Pantheon Type Ia supernovae (SNe Ia), and DES weak lensing and clustering measurements, all multiple-parameter extensions remain consistent with a $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. Regardless of cosmological model, the precision on each of the three parameters, ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{\ensuremath{\Lambda}}}$, ${H}_{0}$, and ${\ensuremath{\sigma}}_{8}$, remains at roughly 1%, showing changes of less than 0.6% in the central values between models. In a model that allows for free curvature and a time-evolving equation of state for dark energy, the combined samples produce a constraint ${\mathrm{\ensuremath{\Omega}}}_{k}=\ensuremath{-}0.0022\ifmmode\pm\else\textpm\fi{}0.0022$. The dark energy constraints lead to ${w}_{0}=\ensuremath{-}0.909\ifmmode\pm\else\textpm\fi{}0.081$ and ${w}_{a}=\ensuremath{-}0.4{9}_{\ensuremath{-}0.30}^{+0.35}$, corresponding to an equation of state of ${w}_{p}=\ensuremath{-}1.018\ifmmode\pm\else\textpm\fi{}0.032$ at a pivot redshift ${z}_{p}=0.29$ and a Dark Energy Task Force Figure of Merit of 94. The inverse distance ladder measurement under this model yields ${H}_{0}=68.18\ifmmode\pm\else\textpm\fi{}0.79\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$, remaining in tension with several direct determination methods; the BAO data allow Hubble constant estimates that are robust against the assumption of the cosmological model. In addition, the BAO data allow estimates of ${H}_{0}$ that are independent of the CMB data, with similar central values and precision under a $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. Our most constraining combination of data gives the upper limit on the sum of neutrino masses at $\ensuremath{\sum}{m}_{\ensuremath{\nu}}<0.115\text{ }\text{ }\mathrm{eV}$ (95% confidence). Finally, we consider the improvements in cosmology constraints over the last decade by comparing our results to a sample representative of the period 2000--2010. We compute the relative gain across the five dimensions spanned by $w$, ${\mathrm{\ensuremath{\Omega}}}_{k}$, $\ensuremath{\sum}{m}_{\ensuremath{\nu}}$, ${H}_{0}$, and ${\ensuremath{\sigma}}_{8}$ and find that the SDSS BAO and RSD data reduce the total posterior volume by a factor of 40 relative to the previous generation. Adding again the Planck, DES, and Pantheon SN Ia samples leads to an overall contraction in the five-dimensional posterior volume of 3 orders of magnitude.

We report a detection of the baryon acousticoscillation (BAO) feature in the flux-correlation function of the Lyα forest of high-redshift quasars with a statistical significance of five standard deviations. The study uses 137 562 quasars in the redshift range 2.1 ≤ z ≤ 3.5 from the data release 11 (DR11) of the Baryon Oscillation Spectroscopic Survey (BOSS) of SDSS-III. This sample contains three times the number of quasars used in previous studies. The measured position of the BAO peak determines the angular distance, DA(z = 2.34) and expansion rate, H(z = 2.34), both on a scale set by the sound horizon at the drag epoch, rd. We find DA/rd = 11.28 ± 0.65(1σ)+2.8-1.2 (2σ) and DH/rd = 9.18 ± 0.28(1σ) ± 0.6(2σ) where DH = c/H. The optimal combination, ~DH0.7DA0.3/rd is determined with a precision of ~2%. For the value rd = 147.4 Mpc, consistent with the cosmic microwave background power spectrum measured by Planck, we find DA(z = 2.34) = 1662 ± 96(1σ) Mpc and H(z = 2.34) = 222 ± 7(1σ) km s-1 Mpc-1. Tests with mock catalogs and variations of our analysis procedure have revealed no systematic uncertainties comparable to our statistical errors. Our results agree with the previously reported BAO measurement at the same redshift using the quasar-Lyα forest cross-correlation. The autocorrelation and cross-correlation approaches are complementary because of the quite different impact of redshift-space distortion on the two measurements. The combined constraints from the two correlation functions imply values of DA/rd that are 7% lower and 7% higher for DH/rd than the predictions of a flat ΛCDM cosmological model with the best-fit Planck parameters. With our estimated statistical errors, the significance of this discrepancy is ≈2.5σ.

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-$\ensuremath{\alpha}$ 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 ${H}_{0}=67.3\ifmmode\pm\else\textpm\fi{}1.1\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$, with 1.7% precision. This measurement assumes standard prerecombination physics but is insensitive to assumptions about dark energy or space curvature, so agreement with CMB-based estimates that assume a flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmology is an important corroboration of this minimal cosmological model. For constant dark energy ($\mathrm{\ensuremath{\Lambda}}$), our $\mathrm{BAO}+\mathrm{SN}+\mathrm{CMB}$ combination yields matter density ${\mathrm{\ensuremath{\Omega}}}_{m}=0.301\ifmmode\pm\else\textpm\fi{}0.008$ and curvature ${\mathrm{\ensuremath{\Omega}}}_{k}=\ensuremath{-}0.003\ifmmode\pm\else\textpm\fi{}0.003$. When we allow more general forms of evolving dark energy, the $\mathrm{BAO}+\mathrm{SN}+\mathrm{CMB}$ parameter constraints are always consistent with flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ values at $\ensuremath{\approx}1\ensuremath{\sigma}$. While the overall ${\ensuremath{\chi}}^{2}$ of model fits is satisfactory, the LyaF BAO measurements are in moderate ($2--2.5\ensuremath{\sigma}$) 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 ${H}_{0}$ 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, $\ensuremath{\sum}{m}_{\ensuremath{\nu}}<0.56\text{ }\text{ }\mathrm{eV}$ (95% confidence), improving to $\ensuremath{\sum}{m}_{\ensuremath{\nu}}<0.25\text{ }\text{ }\mathrm{eV}$ if we include the lensing signal in the Planck CMB power spectrum. In a flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model that allows extra relativistic species, our data combination yields ${N}_{\mathrm{eff}}=3.43\ifmmode\pm\else\textpm\fi{}0.26$; while the LyaF BAO data prefer higher ${N}_{\mathrm{eff}}$ when excluding galaxy BAO, the galaxy BAO alone favor ${N}_{\mathrm{eff}}\ensuremath{\approx}3$. 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.

We measure the large-scale cross-correlation of quasars with the Lyα forest absorption, using over 164,000 quasars from Data Release 11 of the SDSS-III Baryon Oscillation Spectroscopic Survey. We extend the previous study of roughly 60,000 quasars from Data Release 9 to larger separations, allowing a measurement of the Baryonic Acoustic Oscillation (BAO) scale along the line of sight c /( H ( z = 2.36) r s ) = 9.0±0.3 and across the line of sight D A ( z = 2.36)/ r s = 10.8±0.4, consistent with CMB and other BAO data. Using the best fit value of the sound horizon from Planck data ( r s = 147.49 Mpc), we can translate these results to a measurement of the Hubble parameter of H ( z = 2.36) = 226±8 km s −1 Mpc −1 and of the angular diameter distance of D A ( z = 2.36) = 1590±60 Mpc. The measured cross-correlation function and an update of the code to fit the BAO scale (baofit) are made publicly available.