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تسجيل مستخدم جديدPlanck 2015 results. XVIII. Background geometry & topology
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Full-sky CMB maps from the 2015 Planck release allow us to detect departures from global isotropy on the largest scales. We present the first searches using CMB polarization for correlations induced by a non-trivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance $chi_{rec}$). We specialize to flat spaces with toroidal and slab topologies, finding that explicit searches for the latter are sensitive to other topologies with antipodal symmetry. These searches yield no detection of a compact topology at a scale below the diameter of the last scattering surface. The limits on the radius $R_i$ of the largest sphere inscribed in the topological domain (at log-likelihood-ratio $Deltaln{L}>-5$ relative to a simply-connected flat Planck best-fit model) are $R_i>0.97chi_{rec}$ for the cubic torus and $R_i>0.56chi_{rec}$ for the slab. The limit for the cubic torus from the matched-circles search is numerically equivalent, $R_i>0.97chi_{rec}$ (99% CL) from polarisation data alone. We also perform a Bayesian search for a Bianchi VII$_h$ geometry. In the non-physical setting where the Bianchi cosmology is decoupled from the standard cosmology, Planck temperature data favour the inclusion of a Bianchi component. However, the cosmological parameters generating this pattern are in strong disagreement with those found from CMB anisotropy data alone. Fitting the induced polarization pattern for this model to Planck data requires an amplitude of $-0.1pm0.04$ compared to +1 if the model were to be correct. In the physical setting where the Bianchi parameters are fit simultaneously with the standard cosmological parameters, we find no evidence for a Bianchi VII$_h$ cosmology and constrain the vorticity of such models to $(omega/H)_0<7.6times10^{-10}$ (95% CL). [Abridged]
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Planck CMB temperature maps allow detection of large-scale departures from homogeneity and isotropy. We search for topology with a fundamental domain nearly intersecting the last scattering surface (comoving distance $chi_r$). For most topologies stu
died the likelihood maximized over orientation shows some preference for multi-connected models just larger than $chi_r$. This effect is also present in simulated realizations of isotropic maps and we interpret it as the alignment of mild anisotropic correlations with chance features in a single realization; such a feature can also exist, in milder form, when the likelihood is marginalized over orientations. Thus marginalized, the limits on the radius $R_i$ of the largest sphere inscribed in a topological domain (at log-likelihood-ratio -5) are: in a flat Universe, $R_i>0.9chi_r$ for the cubic torus (cf. $R_i>0.9chi_r$ at 99% CL for a matched-circles search); $R_i>0.7chi_r$ for the chimney; $R_i>0.5chi_r$ for the slab; in a positively curved Universe, $R_i>1.0chi_r$ for the dodecahedron; $R_i>1.0chi_r$ for the truncated cube; $R_i>0.9chi_r$ for the octahedron. Similar limits apply to alternate topologies. We perform a Bayesian search for an anisotropic Bianchi VII$_h$ geometry. In a non-physical setting where the Bianchi parameters are decoupled from cosmology, Planck data favour a Bianchi component with a Bayes factor of at least 1.5 units of log-evidence: a Bianchi pattern is efficient at accounting for some large-scale anomalies in Planck data. However, the cosmological parameters are in strong disagreement with those found from CMB anisotropy data alone. In the physically motivated setting where the Bianchi parameters are fitted simultaneously with standard cosmological parameters, we find no evidence for a Bianchi VII$_h$ cosmology and constrain the vorticity of such models: $(omega/H)_0<8times10^{-10}$ (95% CL). [Abridged]
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