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.

/pdf/planck-2015-results-xiii-cosmological-parameters-1l3fnrbf1q.pdf

Planck 2015 results. XIII. 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.

/pdf/the-cosmological-constant-and-dark-energy-1w78acsak0.pdf

The Cosmological Constant and Dark Energy

Recent observations of Type 1a supernovae indicating an accelerating universe have once more drawn attention to the possible existence, at the present epoch, of a small positive Λ-term (cosmological constant). In this paper we review both observational and theoretical aspects of a small cosmological Λ-term. We discuss the current observational situation focusing on cosmological tests of Λ including the age of the universe, high redshift supernovae, gravitational lensing, galaxy clustering and the cosmic microwave background. We also review the theoretical debate surrounding Λ: the generation of Λ in models with spontaneous symmetry breaking and through quantum vacuum polarization effects — mechanisms which are known to give rise to a large value of Λ hence leading to the "cosmological constant problem." More recent attempts to generate a small cosmological constant at the present epoch using either field theoretic techniques, or by modelling a dynamical Λ-term by scalar fields are also extensively discussed. Anthropic arguments favouring a small Λ-term are briefly reviewed. A comprehensive bibliography of recent work on Λ is provided.

http://cds.cern.ch/record/385991/files/9904398.pdf

The Case for a Positive Cosmological Λ-Term

This is a review of the physics and cosmology of the cosmological constant. Focusing on recent developments, I present a pedagogical overview of cosmology in the presence of a cosmological constant, observational constraints on its magnitude, and the physics of a small (and potentially nonzero) vacuum energy.

/pdf/the-cosmological-constant-4ljm1nl1cq.pdf

The Cosmological Constant

We have refined the analysis of the data from the FIRAS (Far-InfraRed Absolute Spectrophotometer) on board the COBE (COsmic Background Explorer). The FIRAS measures the difference between the cosmic microwave background and a precise blackbody spectrum. We find new, tighter upper limits on general deviations from a blackbody spectrum. The rms deviations are less than 50 parts per million of the peak of the cosmic microwave background radiation. For the Comptonization and chemical potential, we find |y| < 15 × 10–6 and |μ| < 9 × 10–5 (95% confidence level [CL]). There are also refinements in the absolute temperature, 2.728 ± 0.004 K (95% CL), the dipole direction, (1, b)/(26414 ± 0.30, 4826 ± 0.30) (95% CL), and the amplitude, 3.372 ± 0.014 mK (95% CL). All of these results agree with our previous publications.

https://iopscience.iop.org/article/10.1086/178173/pdf

The Cosmic Microwave Background spectrum from the full COBE FIRAS data set

The Far-Infrared Absolute Spectrophotometer (FIRAS) on the COBE satellite has conducted an unbiased survey of the far-infrared emission from our Galaxy. The first results of this survey were reported by Wright et al. (1991). We report the results of new analyses of this spectral survey, which includes emission lines from 158 micrometer C(+), 122 and 205 micrometer N(+), 370 and 609 micrometer C(0), and CO J = 2 goes to 1 through J = 5 goes to 4. We report the morphological distribution along the Galactic plane (b = 0 deg) of the spectral line emission, and the high Galactic latitude intensities of the C(+) and 205 micrometer N(+) emission. In the Galactic plane the 205 micrometer line of N(+) generally follows the 158 micrometer C(+) line distribution, but the intensities scale as I(N(+) 205 micrometer) varies as I(C(+) 158 micrometer)(exp 1.5) toward the inner Galaxy. The high Galactic latitude intensity of the 158 micrometer fine-structure transition from C(+) is I(C(+) 158 micrometer) = (1.43 +/- 0.12) x 10(exp -6) csc (absolute value of b) ergs/sq cm s sr for absolute value of b greater than 15 deg, and it decreases more rapidly than the far-infrared intensity with increasing Galactic latitude. C(+) and neutral atomic hydrogen emission are closely correlated with a C(+) cooling rate of (2.65 +/- 0.15) x 10(exp -26) ergs/s. We conclude that this emission arises almost entirely from the cold neutral medium. The high Galactic latitude intensity of the 205 micrometer fine-structure transition from N(+) is I(N(+) 205 micrometer) = (4 +/- 1) x 10(exp -8) csc (absolute value of b) ergs/((sq cm)(s)(sr)) arising entirely from the warm ionized medium. We estimate the total ionizing photon rate in the Galaxy to be phi = 3.5 x 10(exp 53) ionizing photons per second, based on the 205 micrometer N(+) transition.

Morphology of the interstellar cooling lines detected by cobe

We have refined the analysis of the data from the FIRAS (Far InfraRed Absolute Spectrophotometer) on board the COBE (COsmic Background Explorer). The FIRAS measures the difference between the cosmic microwave background and a precise blackbody spectrum. We find new tighter upper limits on general deviations from a blackbody spectrum. The RMS deviations are less than 50 parts per million of the peak of the CMBR. For the Comptonization and chemical potential we find $|y| < 15\times10^{-6}$ and $|\mu| < 9\times10^{-5}$ (95\% CL). There are also refinements in the absolute temperature, 2.728 $\pm$ 0.004 K (95\% CL), and dipole direction, $(\ell,b)=(264.14^\circ\pm0.30, 48.26^\circ\pm0.30)$ (95\% CL), and amplitude, $3.372 \pm 0.007$ mK (95\% CL). All of these results agree with our previous publications.

The Cosmic Microwave Background Spectrum from the Full COBE/FIRAS Data Set

The FIRAS instrument on the COBE satellite has conducted an unbiased survey of the far-infrared emission from our Galaxy. The first results of this survey were reported by Wright et al. (1991). We report the results of new analyses of this spectral survey, which includes emission lines from 158 um C+, 122 um and 205 um N+, 370 um and 609 um C, and CO J=2-1 through 5-4. We report the morphological distribution along the galactic plane (b=0) of the spectral line emission, and the high galactic latitude intensities of the C+ and 205 um N+ emission. The high galactic latitude intensity cosecant of the 158 um fine structure transition from C+ is presented, and C+ is seen to decrease more rapidly than the far infrared intensity with increasing galactic latitude. C+ and H I emission are closely correlated with a C+ cooling rate of (2.65 +/- 0.15)x10^{-26} erg/s/H-atom. We conclude that this emission arises almost entirely from the Cold Neutral Medium. The high galactic latitude intensity of the 205 um fine structure transition from N+ arises entirely from the Warm Ionized Medium, and its cosecant is presented. We estimate the total ionizing photon rate in the Galaxy to be 3.5x10^{53} ionizing photons per second, based on the 205 um N+ transition.

J.M. Gales

Papers

The Cosmic Microwave Background spectrum from the full COBE FIRAS data set

Morphology of the interstellar cooling lines detected by cobe

The Cosmic Microwave Background Spectrum from the Full COBE/FIRAS Data Set

Morphology of the Interstellar Cooling Lines Detected by COBE