Planck 2015 results. XVIII. Background geometry and topology of the Universe
Abstract
Maps of cosmic microwave background (CMB) temperature and polarization from the 2015 release of Planck data provide the highestquality fullsky view of the surface of last scattering available to date. This enables us to detect possible departures from a globally isotropic cosmology. We present the first searches using CMB polarization for correlations induced by a possible nontrivial topology with a fundamental domain that intersects, or nearly intersects, the lastscattering surface (at comoving distance χ_{rec}), both via a direct scan for matched circular patterns at the intersections and by an optimal likelihood calculation for specific topologies. We specialize to flat spaces with cubic toroidal (T3) and slab (T1) 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 with a scale below the diameter of the lastscattering surface. The limits on the radius ℛ_{I} of the largest sphere inscribed in the fundamental domain (at loglikelihood ratio ∆lnℒ > 5 relative to a simplyconnected flat Planck bestfit model) are: ℛ_{I} > 0.97 χ_{rec} for the T3 cubic torus; and ℛ_{I} > 0.56 χ_{rec} for the T1 slab. The limit for the T3 cubic torus from the matchedcircles search is numerically equivalent, ℛ_{I} > 0.97 χ_{rec} at 99% confidence level from polarization data alone. 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 temperature data favour the inclusion of a Bianchi component with a Bayes factor of at least 2.3 units of logevidence. However, the cosmological parameters that generate this pattern are in strong disagreement with those found from CMB anisotropy data alone. Fitting the induced polarization pattern for this model to the Planck data requires an amplitude of 0.10 ± 0.04 compared to the value of + 1 if the model were to be correct. 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} < 7.6 × 10^{10} (95% CL).
 Publication:

Astronomy and Astrophysics
 Pub Date:
 September 2016
 DOI:
 10.1051/00046361/201525829
 arXiv:
 arXiv:1502.01593
 Bibcode:
 2016A&A...594A..18P
 Keywords:

 cosmic background radiation;
 cosmology: observations;
 cosmological parameters;
 gravitation;
 methods: data analysis;
 methods: statistical;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 This paper is one of a set associated with the 2015 data release from Planck (see http://www.cosmos.esa.int/web/planck/publications). 22 Pages, 19 Figures. Accepted for publication in A&