This paper presents the first cosmological results based on Planck measurements of the cosmic microwave background (CMB) temperature and lensing-potential power spectra. We find that the Planck spectra at high multipoles (l ≳ 40) are extremely well described by the standard spatially-flat six-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations. Within the context of this cosmology, the Planck data determine the cosmological parameters to high precision: the angular size of the sound horizon at recombination, the physical densities of baryons and cold dark matter, and the scalar spectral index are estimated to be θ∗ = (1.04147 ± 0.00062) × 10-2, Ωbh2 = 0.02205 ± 0.00028, Ωch2 = 0.1199 ± 0.0027, and ns = 0.9603 ± 0.0073, respectively(note that in this abstract we quote 68% errors on measured parameters and 95% upper limits on other parameters). For this cosmology, we find a low value of the Hubble constant, H0 = (67.3 ± 1.2) km s-1 Mpc-1, and a high value of the matter density parameter, Ωm = 0.315 ± 0.017. These values are in tension with recent direct measurements of H0 and the magnitude-redshift relation for Type Ia supernovae, but are in excellent agreement with geometrical constraints from baryon acoustic oscillation (BAO) surveys. Including curvature, we find that the Universe is consistent with spatial flatness to percent level precision using Planck CMB data alone. We use high-resolution CMB data together with Planck to provide greater control on extragalactic foreground components in an investigation of extensions to the six-parameter ΛCDM model. We present selected results from a large grid of cosmological models, using a range of additional astrophysical data sets in addition to Planck and high-resolution CMB data. None of these models are favoured over the standard six-parameter ΛCDM cosmology. The deviation of the scalar spectral index from unity isinsensitive to the addition of tensor modes and to changes in the matter content of the Universe. We find an upper limit of r0.002< 0.11 on the tensor-to-scalar ratio. There is no evidence for additional neutrino-like relativistic particles beyond the three families of neutrinos in the standard model. Using BAO and CMB data, we find Neff = 3.30 ± 0.27 for the effective number of relativistic degrees of freedom, and an upper limit of 0.23 eV for the sum of neutrino masses. Our results are in excellent agreement with big bang nucleosynthesis and the standard value of Neff = 3.046. We find no evidence for dynamical dark energy; using BAO and CMB data, the dark energy equation of state parameter is constrained to be w = -1.13-0.10+0.13. We also use the Planck data to set limits on a possible variation of the fine-structure constant, dark matter annihilation and primordial magnetic fields. Despite the success of the six-parameter ΛCDM model in describing the Planck data at high multipoles, we note that this cosmology does not provide a good fit to the temperature power spectrum at low multipoles. The unusual shape of the spectrum in the multipole range 20 ≲ l ≲ 40 was seen previously in the WMAP data and is a real feature of the primordial CMB anisotropies. The poor fit to the spectrum at low multipoles is not of decisive significance, but is an “anomaly” in an otherwise self-consistent analysis of the Planck temperature data.

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Planck 2013 results. XVI. Cosmological parameters

Physics welcomes the idea that space contains energy whose gravitational effect approximates that of Einstein's cosmological constant, \ensuremath{\Lambda}; today the concept is termed dark energy or quintessence. Physics also suggests that dark energy could be dynamical, allowing for the arguably appealing picture of an evolving dark-energy density approaching its natural value, zero, and small now because the expanding universe is old. This would alleviate the classical problem of the curious energy scale of a millielectron volt associated with a constant \ensuremath{\Lambda}. Dark energy may have been detected by recent cosmological tests. These tests make a good scientific case for the context, in the relativistic Friedmann-Lema\^{\i}tre model, in which the gravitational inverse-square law is applied to the scales of cosmology. We have well-checked evidence that the mean mass density is not much more than one-quarter of the critical Einstein--de Sitter value. The case for detection of dark energy is not yet as convincing but still serious; we await more data, which may be derived from work in progress. Planned observations may detect the evolution of the dark-energy density; a positive result would be a considerable stimulus for attempts at understanding the microphysics of dark energy. This review presents the basic physics and astronomy of the subject, reviews the history of ideas, assesses the state of the observational evidence, and comments on recent developments in the search for a fundamental theory.

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The Cosmological Constant and Dark Energy

We present cosmological parameter results from the ﬁnal full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to signiﬁcant gains in the precision of other correlated parameters Improved modelling of the small-scale polarization leads to more robust constraints on manyparameters,withresidualmodellinguncertaintiesestimatedtoaﬀectthemonlyatthe05σlevelWeﬁndgoodconsistencywiththestandard spatially-ﬂat6-parameter ΛCDMcosmologyhavingapower-lawspectrumofadiabaticscalarperturbations(denoted“base ΛCDM”inthispaper), from polarization, temperature, and lensing, separately and in combination A combined analysis gives dark matter density Ωch2 = 0120±0001, baryon density Ωbh2 = 00224±00001, scalar spectral index ns = 0965±0004, and optical depth τ = 0054±0007 (in this abstract we quote 68% conﬁdence regions on measured parameters and 95% on upper limits) The angular acoustic scale is measured to 003% precision, with 100θ∗ = 10411±00003Theseresultsareonlyweaklydependentonthecosmologicalmodelandremainstable,withsomewhatincreasederrors, in many commonly considered extensions Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: HubbleconstantH0 = (674±05)kms−1Mpc−1;matterdensityparameterΩm = 0315±0007;andmatterﬂuctuationamplitudeσ8 = 0811±0006 We ﬁnd no compelling evidence for extensions to the base-ΛCDM model Combining with baryon acoustic oscillation (BAO) measurements (and consideringsingle-parameterextensions)weconstraintheeﬀectiveextrarelativisticdegreesoffreedomtobe Neﬀ = 299±017,inagreementwith the Standard Model prediction Neﬀ = 3046, and ﬁnd that the neutrino mass is tightly constrained toPmν < 012 eV The CMB spectra continue to prefer higher lensing amplitudesthan predicted in base ΛCDM at over 2σ, which pulls some parameters that aﬀect thelensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAOdataThejointconstraintwithBAOmeasurementsonspatialcurvatureisconsistentwithaﬂatuniverse, ΩK = 0001±0002Alsocombining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w0 = −103±003, consistent with a cosmological constant We ﬁnd no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r0002 < 006 Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations The Planck base-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey’s combined-probe results including galaxy clustering (which prefers lower ﬂuctuation amplitudes or matter density parameters), and in signiﬁcant, 36σ, tension with local measurements of the Hubble constant (which prefer a higher value) Simple model extensions that can partially resolve these tensions are not favoured by the Planck data

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Planck 2018 results. VI. Cosmological parameters

We present the large-scale correlation function measured from a spectroscopic sample of 46,748 luminous red galaxies from the Sloan Digital Sky Survey. The survey region covers 0.72h −3 Gpc 3 over 3816 square degrees and 0.16 < z < 0.47, making it the best sample yet for the study of large-scale structure. We find a well-detected peak in the correlation function at 100h −1 Mpc separation that is an excellent match to the predicted shape and location of the imprint of the recombination-epoch acoustic oscillations on the low-redshift clustering of matter. This detection demonstrates the linear growth of structure by gravitational instability between z ≈ 1000 and the present and confirms a firm prediction of the standard cosmological theory. The acoustic peak provides a standard ruler by which we can measure the ratio of the distances to z = 0.35 and z = 1089 to 4% fractional accuracy and the absolute distance to z = 0.35 to 5% accuracy. From the overall shape of the correlation function, we measure the matter density mh 2 to 8% and find agreement with the value from cosmic microwave background (CMB) anisotropies. Independent of the constraints provided by the CMB acoustic scale, we find m = 0.273 ±0.025+0.123(1+ w0)+0.137K. Including the CMB acoustic scale, we find that the spatial curvature is K = −0.010 ± 0.009 if the dark energy is a cosmological constant. More generally, our results provide a measurement of cosmological distance, and hence an argument for dark energy, based on a geometric method with the same simple physics as the microwave background anisotropies. The standard cosmological model convincingly passes these new and robust tests of its fundamental properties. Subject headings: cosmology: observations — large-scale structure of the universe — distance scale — cosmological parameters — cosmic microwave background — galaxies: elliptical and lenticular, cD

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Detection of the baryon acoustic peak in the large-scale correlation function of SDSS luminous red galaxies

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

We constrain flat cosmological models with a joint likelihood analysis of a new compilation of data from the cosmic microwave background (CMB) and from the 2dF Galaxy Redshift Survey (2dFGRS). Fitting the CMB alone yields a known degeneracy between the Hubble constant h and the matter density Omega(m), which arises mainly from preserving the location of the peaks in the angular power spectrum. This 'horizon-angle degeneracy' is considered in some detail and is shown to follow the simple relation Omega(m) h(3.4) = constant. Adding the 2dFGRS power spectrum constrains Omega(m) h and breaks the degeneracy. If tensor anisotropies are assumed to be negligible, we obtain values for the Hubble constant of h = 0.665 +/- 0.047, the matter density Omega(m) = 0.313 +/- 0.055, and the physical cold dark matter and baryon densities Omega(c)h(2) = 0.115 +/- 0.009, Omega(b)h(2) = 0.022 +/- 0.002 (standard rms errors). Including a possible tensor component causes very little change to these figures; we set an upper limit to the tensor-to-scalar ratio of r < 0.7 at a 95 per cent confidence level. We then show how these data can be used to constrain the equation of state of the vacuum, and find w < -0.52 at 95 per cent confidence. The preferred cosmological model is thus very well specified, and we discuss the precision with which future CMB data can be predicted, given the model assumptions. The 2dFGRS power-spectrum data and covariance matrix, and the CMB data compilation used here, are available from http://www.roe.ac.uk/similar towjp/.

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S. Moody

Papers

Parameter constraints for flat cosmologies from cosmic microwave background and 2dFGRS power spectra