Planck 2013 results. XXVI. Background geometry and topology of the Universe
Abstract
The new cosmic microwave background (CMB) temperature maps from Planck provide the highestquality fullsky view of the surface of last scattering available to date. This allows us to detect possible departures from the standard model of a globally homogeneous and isotropic cosmology on the largest scales. We search for correlations induced by a possible nontrivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance χ_{rec}), both via a direct search for matched circular patterns at the intersections and by an optimal likelihood search for specific topologies. For the latter we consider flat spaces with cubic toroidal (T3), equalsided chimney (T2) and slab (T1) topologies, three multiconnected spaces of constant positive curvature (dodecahedral, truncated cube and octahedral) and two compact negativecurvature spaces. These searches yield no detection of the compact topology with the scale below the diameter of the last scattering surface. For most compact topologies studied the likelihood maximized over the orientation of the space relative to the observed map shows some preference for multiconnected models just larger than the diameter of the last scattering surface. Since this effect is also present in simulated realizations of isotropic maps, we interpret it as the inevitable alignment of mild anisotropic correlations with chance features in a single sky realization; such a feature can also be present, 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 topological domain (at loglikelihoodratio ∆ln ℒ > 5 relative to a simplyconnected flat Planck bestfit model) are: in a flat Universe, ℛ_{i}> 0.92χ_{rec} for the T3 cubic torus; ℛ_{i}> 0.71χ_{rec} for the T2 chimney; ℛ_{i}> 0.50χ_{rec} for the T1 slab; and in a positively curved Universe, ℛ_{i}> 1.03χ_{rec} for the dodecahedral space; ℛ_{i}> 1.0χ_{rec} for the truncated cube; and ℛ_{i}> 0.89χ_{rec} for the octahedral space. The limit for a wider class of topologies, i.e., those predicting matching pairs of backtoback circles, among them tori and the three spherical cases listed above, coming from the matchedcircles search, is ℛ_{i}> 0.94χ_{rec} at 99% confidence level. Similar limits apply to a wide, although not exhaustive, range of topologies. We also perform a Bayesian search for an anisotropic global Bianchi VII_{h} geometry. In the nonphysical setting where the Bianchi cosmology is decoupled from the standard cosmology, Planck data favour the inclusion of a Bianchi component with a Bayes factor of at least 1.5 units of logevidence. Indeed, the Bianchi pattern is quite efficient at accounting for some of the largescale anomalies found in Planck data. However, the cosmological parameters that generate this pattern are in strong disagreement with those found from CMB anisotropy data alone. In the physically motivated setting where the Bianchi parameters are coupled and fitted simultaneously with the standard cosmological parameters, we find no evidence for a Bianchi VII_{h} cosmology and constrain the vorticity of such models to (ω/H)_{0}< 8.1 × 10^{10} (95% confidence level).
 Publication:

Astronomy and Astrophysics
 Pub Date:
 November 2014
 DOI:
 10.1051/00046361/201321546
 arXiv:
 arXiv:1303.5086
 Bibcode:
 2014A&A...571A..26P
 Keywords:

 cosmology: observations;
 cosmic background radiation;
 cosmological parameters;
 gravitation;
 methods: data analysis;
 methods: statistical;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 24 Pages, 22 Figures