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, H 0 = (67.8 ± 0.9) km s −1 Mpc −1 , a matter density parameter Ω m = 0.308 ± 0.012, and a tilted scalar spectral index with n s = 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 z re = 8.8+1.7 −1.4 . 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 N eff = 3.15 ± 0.23 for the effective number of relativistic degrees of freedom, consistent with the value N eff = 3.046 of the Standard Model of particle physics. The sum of neutrino masses is constrained to m ν < 0.23 eV. The spatial curvature of our Universe is found to be very close to zero, with |Ω K | < 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 r 0.002 < 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 r 0.002 < 0.09 and disfavours inflationary models with a V(φ) ∝ φ 2 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 Corresponding author: G. Efstathiou, e-mail: gpe@ast.cam.ac.ukArticle published by EDP Sciences A13, page 1 of 63 A&A 594, A13 (2016) value for a cosmological constant. The standard big bang nucleosynthesis predictions for the helium and deuterium abundanc...

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 many parameters, with residual modelling uncertainties estimated to affect them only at the 0.5σ level. We find good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted “base ΛCDM” in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Ωch2 = 0.120 ± 0.001, baryon density Ωbh2 = 0.0224 ± 0.0001, scalar spectral index ns = 0.965 ± 0.004, and optical depth τ = 0.054 ± 0.007 (in this abstract we quote 68% confidence regions on measured parameters and 95% on upper limits). The angular acoustic scale is measured to 0.03% precision, with 100θ* = 1.0411 ± 0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: Hubble constant H0 = (67.4 ± 0.5)  km s−1 Mpc−1; matter density parameter Ωm = 0.315 ± 0.007; and matter fluctuation amplitude σ8 = 0.811 ± 0.006. We find no compelling evidence for extensions to the base-ΛCDM model. Combining with baryon acoustic oscillation (BAO) measurements (and considering single-parameter extensions) we constrain the effective extra relativistic degrees of freedom to be Neff = 2.99 ± 0.17, in agreement with the Standard Model prediction Neff = 3.046, and find that the neutrino mass is tightly constrained to ∑mν <  0.12  eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base ΛCDM at over 2σ, which pulls some parameters that affect the lensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, ΩK = 0.001 ± 0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w0 = −1.03 ± 0.03, 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 r0.002 <  0.06. 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, 3.6σ, 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.

We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. We start with cases where the DE only directly affects the background evolution, considering Taylor expansions of the equation of state w(a), as well as principal component analysis and parameterizations related to the potential of a minimally coupled DE scalar field. When estimating the density of DE at early times, we significantly improve present constraints and find that it has to be below ∼2% (at 95% confidence) of the critical density, even when forced to play a role for z < 50 only. We then move to general parameterizations of the DE or MG perturbations that encompass both effective field theories and the phenomenology of gravitational potentials in MG models. Lastly, we test a range of specific models, such as k-essence, f (R) theories, and coupled DE. In addition to the latest Planck data, for our main analyses, we use background constraints from baryonic acoustic oscillations, type-Ia supernovae, and local measurements of the Hubble constant. We further show the impact of measurements of the cosmological perturbations, such as redshift-space distortions and weak gravitational lensing. These additional probes are important tools for testing MG models and for breaking degeneracies that are still present in the combination of Planck and background data sets. All results that include only background parameterizations (expansion of the equation of state, early DE, general potentials in minimally-coupled scalar fields or principal component analysis) are in agreement with ΛCDM. When testing models that also change perturbations (even when the background is fixed to ΛCDM), some tensions appear in a few scenarios: the maximum one found is ∼2σ for Planck TT+lowP when parameterizing observables related to the gravitational potentials with a chosen time dependence; the tension increases to, at most, 3σ when external data sets are included. It however disappears when including CMB lensing.

The European Space Agency's Planck satellite, which is dedicated to studying the early Universe and its subsequent evolution, was launched on 14 May 2009. It scanned the microwave and submillimetre sky continuously between 12 August 2009 and 23 October 2013. In February 2015, ESA and the Planck Collaboration released the second set of cosmology products based on data from the entire Planck mission, including both temperature and polarization, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper gives an overview of the main characteristics of the data and the data products in the release, as well as the associated cosmological and astrophysical science results and papers. The data products include maps of the cosmic microwave background (CMB), the thermal Sunyaev-Zeldovich effect, diffuse foregrounds in temperature and polarization, catalogues of compact Galactic and extragalactic sources (including separate catalogues of Corresponding author: C. R. Lawrence, e-mail: charles.lawrence@jpl.nasa.govArticle published by EDP Sciences A1, page 1 of 38 A&A 594, A1 (2016) Sunyaev-Zeldovich clusters and Galactic cold clumps), and extensive simulations of signals and noise used in assessing uncertainties and the performance of the analysis methods. The likelihood code used to assess cosmological models against the Planck data is described, along with a CMB lensing likelihood. Scientific results include cosmological parameters derived from CMB power spectra, gravitational lensing, and cluster counts, as well as constraints on inflation, non-Gaussianity, primordial magnetic fields, dark energy, and modified gravity, and new results on low-frequency Galactic foregrounds.

General Relativity and the ΛCDM framework are currently the standard lore and constitute the concordance paradigm. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology the last two decades, offer the motivation and lead a large amount of research to be devoted in constructing various extensions and modifications.All extended theories and scenarios are first examined under the light of theoretical consistency, and then are applied to various geometrical backgrounds, such as the cosmological and the spherical symmetric ones. Their predictions at both the background and perturbation levels, and concerning cosmology at early, intermediate and late times, are then confronted with the huge amount of observational data that astrophysics and cosmology are able to offer recently. Theories, scenarios and models that successfully and efficiently pass the above steps are classified as viable and are candidates for the description of Nature.We list the recent developments in the fields of gravity and cosmology, presenting the state of the art, high-lighting the open problems, and outlining the directions of future research.

We study the effects of modified theories of gravity on the cosmic microwave background (CMB) anisotropies power spectrum, and in particular on its large scales, where the integrated SachsWolfe (ISW) effect is important. Starting with a general parametrisation, we then specialise to f (R) theories and theories with Yukawa-type interactions between dark matter particles. In these models, the evolution of the metric potentials is altered, and the contribution to the ISW effect can differ significantly from that in the standard model of cosmology. We proceed to compare these predictions with observational data for the CMB and the ISW, performing a full Monte Carlo Markov chain (MCMC) analysis. In the case of f (R) theories, the result is an upper limit on the lengthscale associated to the extra scalar degree of freedom characterising these theories. With the addition of data from the Hubble diagram of Type Ia supernovae, we obtain an upper limit on the lengthscale of the theory of B0 < 0.4, or correspondingly λ1 < 1900 Mpc/h at 95% c.l. improving previous CMB constraints. For Yukawa-type models we get a bound on the coupling 0.75 < β1 < 1.25 at the 95% c.l. We also discuss the implications of the assumed priors on the estimation of modified gravity parameters, showing that a marginally less conservative choice improves the f (R) constraints to λ1 < 1400 Mpc/h, corresponding to B0 < 0.2 at 95% c.l.

We investigate an interacting dark sector scenario in which the vacuum energy is free to interact with cold dark matter (CDM), which itself is assumed to cluster under the sole action of gravity, i.e. it is in free fall (geodesic), as in ΛCDM. The interaction is characterised by a dimensionless coupling q V (z), in general a function of redshift. Aiming to reconstruct the evolution of the coupling, we use CMB data from Planck 2015, along with baryon acoustic oscillation, redshift space distortion and Type Ia supernova measurements to constrain various parametrizations of q V (z). We present the full linear perturbation theory of this interacting scenario and use MCMC sampling to study five different cases: two cases in which we have ΛCDM evolution in the distant past, until a set redshift z trans , below which the interaction switches on and q V is the single sampled parameter, with z trans fixed at z trans = 3000 and z trans = 0.9 respectively; a case where we allow this transition redshift to vary along with q V ; a case in which the vacuum energy is zero for z > z trans and then begins to grow once the interaction switches on; and the final case in which we bin q V (z) in four redshift bins to investigate the possibility of a dynamical interaction, reconstructing the redshift evolution of the function using Gaussian processes. We find that, in all cases where the high redshift evolution is not modified, the results are compatible with a vanishing coupling, thus finding no significant deviation from ΛCDM.

Modified Gravity theories generally affect the Poisson equation and the gravitational slip (effective anisotropic stress) in an observable way, that can be parameterized by two generic functions (η and µ) of time and space. We bin the time dependence of these functions in redshift and present forecasts on each bin for future surveys like Euclid. We consider both Galaxy Clustering and Weak Lensing surveys, showing the impact of the non-linear regime, treated with two different semi-analytical approximations. In addition to these future observables, we use a prior covariance matrix derived from the Planck observations of the Cosmic Microwave Background. Our results show that η and µ in different redshift bins are significantly correlated, but including non-linear scales reduces or even eliminates the correlation, breaking the degeneracy between Modified Gravity parameters and the overall amplitude of the matter power spectrum. We further decorrelate parameters with a Zerophase Component Analysis and identify which combinations of the Modified Gravity parameter amplitudes, in different redshift bins, are best constrained by future surveys. We also extend the analysis to two particular parameterizations of the time evolution of µ and η and consider, in addition to Euclid, also SKA1, SKA2, DESI: we find in this case that future surveys will be able to constrain the current values of η and µ at the 2-5% level when using only linear scales (wavevector k < 0.15 h/Mpc), depending on the specific time parameterization; sensitivity improves to about 1% when non-linearities are included. CONTENTS