Planck2015 results

Abstract

We test the statistical isotropy and Gaussianity of the cosmic microwave background (CMB) anisotropies using observations made by the Planck satellite. Our results are based mainly on the full Planck mission for temperature, but also include some polarization measurements. In particular, we consider the CMB anisotropy maps derived from the multi-frequency Planck data by several component-separation methods. For the temperature anisotropies, we find excellent agreement between results based on these sky maps over both a very large fraction of the sky and a broad range of angular scales, establishing that potential foreground residuals do not affect our studies. Tests of skewness, kurtosis, multi-normality, N-point functions, and Minkowski functionals indicate consistency with Gaussianity, while a power deficit at large angular scales is manifested in several ways, for example low map variance. The results of a peak statistics analysis are consistent with the expectations of a Gaussian random field. The "Cold Spot" is detected with several methods, including map kurtosis, peak statistics, and mean temperature profile. We thoroughly probe the large-scale dipolar power asymmetry, detecting it with several independent tests, and address the subject of a posteriori correction. Tests of directionality suggest the presence of angular clustering from large to small scales, but at a significance that is dependent on the details of the approach. We perform the first examination of polarization data, finding the morphology of stacked peaks to be consistent with the expectations of statistically isotropic simulations. Where they overlap, these results are consistent with the Planck 2013 analysis based on the nominal mission data and provide our most thorough view of the statistics of the CMB fluctuations to date.

Quantum corrections to the Mukhanov-Sasaki equations

“…The latest Planck 2015 analysis of the power spectrum of the CMB [2,4] found an excellent agreement with the theoretical predictions of standard cosmology [5] over a broad range of scales. Even so, there are indications of some possible tensions between those predictions and the observations [2,6], especially at large angular scales.…”

“…This dynamical evolution is generated by an operatorĤ 0 that we take to coincide with the square root ofĤ ð2Þ 0 , at least up to terms that, when squared, are negligible compared to the quadratic perturbative contributions of the constraint. 4 The operatorĤ 0 can be regarded as a modification of the evolution generator (along ϕ) of the homogeneous system with a free massless field in order to include a field potential. In summary, we adopt for χ the ansatz χðx; ϕÞ ¼Ûðx; ϕÞχ 0 ðxÞ, where χ 0 is the initial FLRW state at a certain value ϕ 0 of the homogeneous scalar field, andÛ…”

“…Similarly, from the effective constraint on the perturbations and the definition of T, one gets the relation dϕ ¼ ðπ ðinhÞ ϕ þ hĤ 0 i χ ÞdT. Here, 4 If the originalĤ ð2Þ 0 is not positive but just self-adjoint, in practice, for small perturbations and given Eq. (3.1), it suffices to consider the positive part of its spectrum taking projections and proceed then to calculate the square root.…”

Probing cosmic anisotropy with gravitational waves as standard sirens

“…Wilkinson microwave anisotropy probe (WMAP) data analysis [10][11][12][13] and later confirmed in Planck 2013/2015 data analysis [14][15][16]. This hemispherical asymmetry reflects an asymmetric power of one ecliptic hemisphere with respect to the other one, which can be modeled as dipole modulation anisotropy [17,18].…”

“…In Planck 2013 [14], the dipole amplitude is constrained around 0.078 ± 0.021 and the dipole direction is constrained around (l, b) = (227 • , −15 • ) ± 19 • . In Planck 2015 [16], the dipole amplitude is constrained around 0.066 ± 0.021 and the dipole direction is constrained around (l, b) = (230 • , −16 • )±24 • . Besides the temperature data of CMB observations, this dipole anisotropy also manifests itself in polarized data [19,20].…”