This paper presents cosmological results based on full-mission Planck observations of temperature and polarization anisotropies of the cosmic microwave background (CMB) radiation. Our results are in very good agreement with the 2013 analysis of the Planck nominal-mission temperature data, but with increased precision. The temperature and polarization power spectra are consistent with the standard spatially-flat 6-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations (denoted “base ΛCDM” in this paper). From the Planck temperature data combined with Planck lensing, for this cosmology we find a Hubble constant, H0 = (67.8 ± 0.9) km s-1Mpc-1, a matter density parameter Ωm = 0.308 ± 0.012, and a tilted scalar spectral index with ns = 0.968 ± 0.006, consistent with the 2013 analysis. Note that in this abstract we quote 68% confidence limits on measured parameters and 95% upper limits on other parameters. We present the first results of polarization measurements with the Low Frequency Instrument at large angular scales. Combined with the Planck temperature and lensing data, these measurements give a reionization optical depth of τ = 0.066 ± 0.016, corresponding to a reionization redshift of . These results are consistent with those from WMAP polarization measurements cleaned for dust emission using 353-GHz polarization maps from the High Frequency Instrument. We find no evidence for any departure from base ΛCDM in the neutrino sector of the theory; for example, combining Planck observations with other astrophysical data we find Neff = 3.15 ± 0.23 for the effective number of relativistic degrees of freedom, consistent with the value Neff = 3.046 of the Standard Model of particle physics. The sum of neutrino masses is constrained to ∑ mν < 0.23 eV. The spatial curvature of our Universe is found to be very close to zero, with | ΩK | < 0.005. Adding a tensor component as a single-parameter extension to base ΛCDM we find an upper limit on the tensor-to-scalar ratio of r0.002< 0.11, consistent with the Planck 2013 results and consistent with the B-mode polarization constraints from a joint analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP B-mode data to our analysis leads to a tighter constraint of r0.002 < 0.09 and disfavours inflationarymodels with a V(φ) ∝ φ2 potential. The addition of Planck polarization data leads to strong constraints on deviations from a purely adiabatic spectrum of fluctuations. We find no evidence for any contribution from isocurvature perturbations or from cosmic defects. Combining Planck data with other astrophysical data, including Type Ia supernovae, the equation of state of dark energy is constrained to w = −1.006 ± 0.045, consistent with the expected value for a cosmological constant. The standard big bang nucleosynthesis predictions for the helium and deuterium abundances for the best-fit Planck base ΛCDM cosmology are in excellent agreement with observations. We also constraints on annihilating dark matter and on possible deviations from the standard recombination history. In neither case do we find no evidence for new physics. The Planck results for base ΛCDM are in good agreement with baryon acoustic oscillation data and with the JLA sample of Type Ia supernovae. However, as in the 2013 analysis, the amplitude of the fluctuation spectrum is found to be higher than inferred from some analyses of rich cluster counts and weak gravitational lensing. We show that these tensions cannot easily be resolved with simple modifications of the base ΛCDM cosmology. Apart from these tensions, the base ΛCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets.

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Planck 2015 results - XIII. Cosmological parameters

We present results based on full-mission Planck observations of temperature and polarization anisotropies of the CMB. These data are consistent with the six-parameter inflationary LCDM cosmology. From the Planck temperature and lensing data, for this cosmology we find a Hubble constant, H0= (67.8 +/- 0.9) km/s/Mpc, a matter density parameter Omega_m = 0.308 +/- 0.012 and a scalar spectral index with n_s = 0.968 +/- 0.006. (We quote 68% errors on measured parameters and 95% limits on other parameters.) Combined with Planck temperature and lensing data, Planck LFI polarization measurements lead to a reionization optical depth of tau = 0.066 +/- 0.016. Combining Planck with other astrophysical data we find N_ eff = 3.15 +/- 0.23 for the effective number of relativistic degrees of freedom and the sum of neutrino masses is constrained to < 0.23 eV. Spatial curvature is found to be |Omega_K| < 0.005. For LCDM we find a limit on the tensor-to-scalar ratio of r <0.11 consistent with the B-mode constraints from an analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP data leads to a tighter constraint of r < 0.09. We find no evidence for isocurvature perturbations or cosmic defects. The equation of state of dark energy is constrained to w = -1.006 +/- 0.045. Standard big bang nucleosynthesis predictions for the Planck LCDM cosmology are in excellent agreement with observations. We investigate annihilating dark matter and deviations from standard recombination, finding no evidence for new physics. The Planck results for base LCDM are in agreement with BAO data and with the JLA SNe sample. However the amplitude of the fluctuations is found to be higher than inferred from rich cluster counts and weak gravitational lensing. Apart from these tensions, the base LCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets.

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Planck 2015 results. XIII. Cosmological parameters

We analyse the large-scale correlation function of the 6dF Galaxy Survey (6dFGS) and detect a baryon acoustic oscillation (BAO) signal at 105h −1 Mpc. The 6dFGS BAO detection allows us to constrain the distance–redshift relation at zeff = 0.106. We achieve a distance measure of DV (zeff) = 457 ± 27 Mpc and a measurement of the distance ratio, rs(zd)/DV (zeff) = 0.336 ± 0.015 (4.5 per cent precision), where rs(zd) is the sound horizon at the drag epoch zd .T he loweffective redshift of 6dFGS makes it a competitive and independent alternative to Cepheids and low-z supernovae in constraining the Hubble constant. We find a Hubble constant of H0 = 67 ± 3.2 km s −1 Mpc −1 (4.8 per cent precision) that depends only on theWilkinson Microwave Anisotropy Probe-7 (WMAP-7) calibration of the sound horizon and on the galaxy clustering in 6dFGS. Compared to earlier BAO studies at higher redshift, our analysis is less dependent on other cosmological parameters. The sensitivity to H0 can be used to break the degeneracy between the dark energy equation of state parameter w and H0 in the cosmic microwave background data. We determine that w =− 0.97 ± 0.13, using only WMAP-7 and BAO data from both 6dFGS and Percival et al. (2010). We also discuss predictions for the large-scale correlation function of two future wide-angle surveys: the Wide field ASKAP L-band Legacy All-sky Blind surveY (WALLABY) blind H I survey (with the Australian Square Kilometre Array Pathfinder, ASKAP) and the proposed Transforming Astronomical Imaging surveys through Polychromatic Analysis of Nebulae (TAIPAN) all-southern-sky optical galaxy survey with the UK Schmidt Telescope. We find that both surveys are very likely to yield detections of the BAO peak, making WALLABY the first radio galaxy survey to do so. We also predict that TAIPAN has the potential to constrain the Hubble constant with 3 per cent precision.

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The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant

We present a one per cent measurement of the cosmic distance scale from the detections of the baryon acoustic oscillations in the clustering of galaxies from the Baryon Oscillation Spectroscopic Survey (BOSS), which is part of the Sloan Digital Sky Survey III (SDSS-III). Our results come from the Data Release 11 (DR11) sample, containing nearly one million galaxies and covering approximately $8\,500$ square degrees and the redshift range $0.2<z<0.7$. We also compare these results with those from the publicly released DR9 and DR10 samples. Assuming a concordance $\Lambda$CDM cosmological model, the DR11 sample covers a volume of 13\,Gpc${}^3$ and is the largest region of the Universe ever surveyed at this density. We measure the correlation function and power spectrum, including density-field reconstruction of the baryon acoustic oscillation (BAO) feature. The acoustic features are detected at a significance of over $7\,\sigma$ in both the correlation function and power spectrum. Fitting for the position of the acoustic features measures the distance relative to the sound horizon at the drag epoch, $r_d$, which has a value of $r_{d,{\rm fid}}=149.28\,$Mpc in our fiducial cosmology. We find $D_V=(1264\pm25\,{\rm Mpc})(r_d/r_{d,{\rm fid}})$ at $z=0.32$ and $D_V=(2056\pm20\,{\rm Mpc})(r_d/r_{d,{\rm fid}})$ at $z=0.57$. At 1.0 per cent, this latter measure is the most precise distance constraint ever obtained from a galaxy survey. Separating the clustering along and transverse to the line-of-sight yields measurements at $z=0.57$ of $D_A=(1421\pm20\,{\rm Mpc})(r_d/r_{d,{\rm fid}})$ and $H=(96.8\pm3.4\,{\rm km/s/Mpc})(r_{d,{\rm fid}}/r_d)$. Our measurements of the distance scale are in good agreement with previous BAO measurements and with the predictions from cosmic microwave background data for a spatially flat cold dark matter model with a cosmological constant.

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The clustering of galaxies in the sdss-iii baryon oscillation spectroscopic survey: Baryon acoustic oscillations in the data release 9 spectroscopic galaxy sample

The spectroscopic Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) galaxy sample represents the final set of galaxies observed using the original SDSS target selection criteria. We analyse the clustering of galaxies within this sample, including both the luminous red galaxy and main samples, and also include the 2-degree Field Galaxy Redshift Survey data. In total, this sample comprises 893 319 galaxies over 9100 deg(2). Baryon acoustic oscillations (BAO) are observed in power spectra measured for different slices in redshift; this allows us to constrain the distance-redshift relation at multiple epochs. We achieve a distance measure at redshift z = 0.275, of r(s)(z(d))/D-V(0.275) = 0.1390 +/- 0.0037 (2.7 per cent accuracy), where r(s)(z(d)) is the comoving sound horizon at the baryon-drag epoch, D-V(z) equivalent to [(1 + z)(2)D(A)(2)cz/H(z)](1/3), D-A(z) is the angular diameter distance and H(z) is the Hubble parameter. We find an almost independent constraint on the ratio of distances D-V(0.35)/D-V(0.2) = 1.736 +/- 0.065, which is consistent at the 1.1 sigma level with the best-fitting Lambda cold dark matter model obtained when combining our z = 0.275 distance constraint with the Wilkinson Microwave Anisotropy Probe 5-year (WMAP5) data. The offset is similar to that found in previous analyses of the SDSS DR5 sample, but the discrepancy is now of lower significance, a change caused by a revised error analysis and a change in the methodology adopted, as well as the addition of more data. Using WMAP5 constraints on Omega(b)h(2) and Omega(c) h(2), and combining our BAO distance measurements with those from the Union supernova sample, places a tight constraint on Omega(m) = 0.286 +/- 0.018 and H-0 = 68.2 +/- 2.2 km s(-1) Mpc(-1) that is robust to allowing Omega(k) not equal 0 and omega not equal -1. This result is independent of the behaviour of dark energy at redshifts greater than those probed by the BAO and supernova measurements. Combining these data sets with the full WMAP5 likelihood constraints provides tight constraints on both Omega(k) = -0.006 +/- 0.008 and omega = -0.97 +/- 0.10 for a constant dark energy equation of state.

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Baryon Acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample

We calculate the redshift-space power spectrum of the Sloan Digital Sky Survey (SDSS) Data Release 4 (DR4) Luminous Red Galaxy (LRG) sample, finding evidence for a full series of acoustic features down to the scales of \sim 0.2 hMpc^{-1}. This corresponds up to the 7th peak in the CMB angular power spectrum. The acoustic scale derived, (105.4 \pm 2.3) h^{-1}Mpc, agrees very well with the ``concordance'' model prediction and also with the one determined via the analysis of the spatial two-point correlation function by Eisenstein et al. (2005). The models with baryonic features are favored by 3.3 \sigma over their ``smoothed-out'' counterparts without any oscillatory behavior.

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Acoustic oscillations in the SDSS Luminous Red Galaxy sample power spectrum

The PAMELA, Fermi and HESS experiments (PFH) have shown anomalous excesses in the cosmic positron and electron fluxes. A very exciting possibility is that those excesses are due to annihilating dark matter (DM). In this paper we calculate constraints on leptonically annihilating DM using observational data on diffuse extragalactic gamma-ray background and measurements of the optical depth to the last-scattering surface, and compare those with the PFH favored region in the m_{DM} - plane. Having specified the detailed form of the energy input with PYTHIA Monte Carlo tools we solve the radiative transfer equation which allows us to determine the amount of energy being absorbed by the cosmic medium and also the amount left over for the diffuse gamma background. We find that the constraints from the optical depth measurements are able to rule out the PFH favored region fully for the \tau^{-}+\tau^{+} annihilation channel and almost fully for the \mu^{-}+\mu^{+} annihilation channel. It turns out that those constraints are quite robust with almost no dependence on low redshift clustering boost. The constraints from the gamma-ray background are sensitive to the assumed halo concentration model and, for the power law model, rule out the PFH favored region for all leptonic annihilation channels. We also find that it is possible to have models that fully ionize the Universe at low redshifts. However, those models produce too large free electron fractions at z > ~100 and are in conflict with the optical depth measurements. Also, the magnitude of the annihilation cross-section in those cases is larger than suggested by the PFH data.

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Constraints on leptonically annihilating Dark Matter from reionization and extragalactic gamma background

As a test of general relativity on cosmological scales, we measure the \gamma parameter for the growth rate of density perturbations using the redshift-space distortion of the luminous red galaxies in the Sloan Digital Sky Survey (SDSS). Assuming the cosmological constant model, which matches the results of the WMAP experiment, we find \gamma=0.62+1.8(\sigma_8-0.8) \pm 0.11 at 1-sigma confidence level, which is consistent with the prediction of general relativity, \gamma\simeq0.55\sim0.56. Rather high value of \sigma_8(\geq0.87) is required to be consistent with the prediction of the cosmological DGP model, \gamma\simeq0.68.

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Testing general relativity with the multipole spectra of the SDSS luminous red galaxies

In this paper we determine the constraints on cosmological parameters using the CMB data from the WMAP experiment together with the recent power spectrum measurement of the SDSS Luminous Red Galaxies (LRGs). Specifically, we focus on spatially flat, low matter density models with adiabatic Gaussian initial conditions. The spatial flatness is achieved with an additional quintessence component whose equation of state parameter w_eff is taken to be independent of redshift. Throughout most of the paper we do not allow any massive neutrino contribution and also the influence of the gravitational waves on the CMB is taken to be negligible. The analysis is carried out separately for two cases: (i) using the acoustic scale measurements as presented in Hutsi (2006), (ii) using the full SDSS LRG power spectrum and its covariance matrix. We are able to obtain a very tight constraint on the Hubble constant: H_0 = 70.8 ^{+2.1}_{-2.0} km/s/Mpc, which helps in breaking several degeneracies between the parameters and allows us to determine the low redshift expansion law with much higher accuracy than available from the WMAP + HST data alone. The positive deceleration parameter q_0 is found to be ruled out at 5.5 \sigma confidence level. Finally, we extend our analysis by investigating the effects of relaxing the assumption of spatial flatness and also allow for a contribution from massive neutrinos.

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Power spectrum of the SDSS luminous red galaxies: constraints on cosmological parameters

We use the direct Fourier method to calculate the redshift-space power spectrum of the maxBCG cluster catalog -- currently by far the largest existing galaxy cluster sample. The total number of clusters used in our analysis is 12,616. After accounting for the radial smearing effect caused by photometric redshift errors and also introducing a simple treatment for the nonlinear effects, we show that currently favored low matter density "concordance" LCDM cosmology provides a very good fit to the estimated power. Thanks to the large volume (~0.4 h^{-3}Gpc^{3}), high clustering amplitude (linear effective bias parameter b_{eff} ~3x(0.85/sigma_8)), and sufficiently high sampling density (~3x10^{-5} h^{3}Mpc^{-3}) the recovered power spectrum has high enough signal to noise to allow us to find evidence (~2 sigma CL) for the baryonic acoustic oscillations (BAO). In case the clusters are additionally weighted by their richness the resulting power spectrum has slightly higher large-scale amplitude and smaller damping on small scales. As a result the confidence level for the BAO detection is somewhat increased: ~2.5 sigma. The ability to detect BAO with relatively small number of clusters is encouraging in the light of several proposed large cluster surveys.

Gert Huetsi

Papers

Acoustic oscillations in the SDSS Luminous Red Galaxy sample power spectrum

Constraints on leptonically annihilating Dark Matter from reionization and extragalactic gamma background

Testing general relativity with the multipole spectra of the SDSS luminous red galaxies

Power spectrum of the SDSS luminous red galaxies: constraints on cosmological parameters

Power spectrum of the maxBCG sample: detection of acoustic oscillations using galaxy clusters