Planck 2013 results

XXVI. Background geometry and topology of the Universe

Jussi Varis, A.H. Jaffe (Corresponding Author), Planck Collaboration

Research output: Contribution to journalArticleScientificpeer-review

28 Citations (Scopus)

Abstract

The new cosmic microwave background (CMB) temperature maps from Planck provide the highest-quality full-sky 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 non-trivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance ?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), equal-sided chimney (T2) and slab (T1) topologies, three multi-connected spaces of constant positive curvature (dodecahedral, truncated cube and octahedral) and two compact negative-curvature 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 multi-connected 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 Ri of the largest sphere inscribed in topological domain (at log-likelihood-ratio ?ln L > -5 relative to a simply-connected flat Planck best-fit model) are: in a flat Universe, Ri> 0.92?rec for the T3 cubic torus; Ri> 0.71?rec for the T2 chimney; Ri> 0.50?rec for the T1 slab; and in a positively curved Universe, Ri> 1.03?rec for the dodecahedral space; Ri> 1.0?rec for the truncated cube; and Ri> 0.89?rec for the octahedral space. The limit for a wider class of topologies, i.e., those predicting matching pairs of back-to-back circles, among them tori and the three spherical cases listed above, coming from the matched-circles search, is Ri> 0.94?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 VIIh geometry. In the non-physical 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 log-evidence. Indeed, the Bianchi pattern is quite efficient at accounting for some of the large-scale 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 VIIh cosmology and constrain the vorticity of such models to (?/H)0<8.1 * 10-10 (95% confidence level).
Original languageEnglish
Article numberA26
Number of pages23
JournalAstronomy and Astrophysics
Volume571
DOIs
Publication statusPublished - 2014
MoE publication typeA1 Journal article-refereed

Fingerprint

topology
universe
geometry
cosmology
scattering
chimneys
curvature
sky
confidence
slab
slabs
microwaves
likelihood ratio
vorticity
intersections
anisotropy
alignment
inclusions
anomalies
anomaly

Keywords

  • cosmology
  • cosmic background radiation
  • cosmological parameters
  • gravitation
  • data analysis

Cite this

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title = "Planck 2013 results: XXVI. Background geometry and topology of the Universe",
abstract = "The new cosmic microwave background (CMB) temperature maps from Planck provide the highest-quality full-sky 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 non-trivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance ?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), equal-sided chimney (T2) and slab (T1) topologies, three multi-connected spaces of constant positive curvature (dodecahedral, truncated cube and octahedral) and two compact negative-curvature 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 multi-connected 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 Ri of the largest sphere inscribed in topological domain (at log-likelihood-ratio ?ln L > -5 relative to a simply-connected flat Planck best-fit model) are: in a flat Universe, Ri> 0.92?rec for the T3 cubic torus; Ri> 0.71?rec for the T2 chimney; Ri> 0.50?rec for the T1 slab; and in a positively curved Universe, Ri> 1.03?rec for the dodecahedral space; Ri> 1.0?rec for the truncated cube; and Ri> 0.89?rec for the octahedral space. The limit for a wider class of topologies, i.e., those predicting matching pairs of back-to-back circles, among them tori and the three spherical cases listed above, coming from the matched-circles search, is Ri> 0.94?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 VIIh geometry. In the non-physical 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 log-evidence. Indeed, the Bianchi pattern is quite efficient at accounting for some of the large-scale 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 VIIh cosmology and constrain the vorticity of such models to (?/H)0<8.1 * 10-10 (95{\%} confidence level).",
keywords = "cosmology, cosmic background radiation, cosmological parameters, gravitation, data analysis",
author = "Jussi Varis and A.H. Jaffe and {Planck Collaboration}",
note = "Project code: 18080",
year = "2014",
doi = "10.1051/0004-6361/201321546",
language = "English",
volume = "571",
journal = "Astronomy and Astrophysics",
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}

Planck 2013 results : XXVI. Background geometry and topology of the Universe. / Varis, Jussi; Jaffe, A.H. (Corresponding Author); Planck Collaboration.

In: Astronomy and Astrophysics, Vol. 571, A26, 2014.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Planck 2013 results

T2 - XXVI. Background geometry and topology of the Universe

AU - Varis, Jussi

AU - Jaffe, A.H.

AU - Planck Collaboration

N1 - Project code: 18080

PY - 2014

Y1 - 2014

N2 - The new cosmic microwave background (CMB) temperature maps from Planck provide the highest-quality full-sky 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 non-trivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance ?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), equal-sided chimney (T2) and slab (T1) topologies, three multi-connected spaces of constant positive curvature (dodecahedral, truncated cube and octahedral) and two compact negative-curvature 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 multi-connected 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 Ri of the largest sphere inscribed in topological domain (at log-likelihood-ratio ?ln L > -5 relative to a simply-connected flat Planck best-fit model) are: in a flat Universe, Ri> 0.92?rec for the T3 cubic torus; Ri> 0.71?rec for the T2 chimney; Ri> 0.50?rec for the T1 slab; and in a positively curved Universe, Ri> 1.03?rec for the dodecahedral space; Ri> 1.0?rec for the truncated cube; and Ri> 0.89?rec for the octahedral space. The limit for a wider class of topologies, i.e., those predicting matching pairs of back-to-back circles, among them tori and the three spherical cases listed above, coming from the matched-circles search, is Ri> 0.94?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 VIIh geometry. In the non-physical 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 log-evidence. Indeed, the Bianchi pattern is quite efficient at accounting for some of the large-scale 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 VIIh cosmology and constrain the vorticity of such models to (?/H)0<8.1 * 10-10 (95% confidence level).

AB - The new cosmic microwave background (CMB) temperature maps from Planck provide the highest-quality full-sky 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 non-trivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance ?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), equal-sided chimney (T2) and slab (T1) topologies, three multi-connected spaces of constant positive curvature (dodecahedral, truncated cube and octahedral) and two compact negative-curvature 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 multi-connected 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 Ri of the largest sphere inscribed in topological domain (at log-likelihood-ratio ?ln L > -5 relative to a simply-connected flat Planck best-fit model) are: in a flat Universe, Ri> 0.92?rec for the T3 cubic torus; Ri> 0.71?rec for the T2 chimney; Ri> 0.50?rec for the T1 slab; and in a positively curved Universe, Ri> 1.03?rec for the dodecahedral space; Ri> 1.0?rec for the truncated cube; and Ri> 0.89?rec for the octahedral space. The limit for a wider class of topologies, i.e., those predicting matching pairs of back-to-back circles, among them tori and the three spherical cases listed above, coming from the matched-circles search, is Ri> 0.94?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 VIIh geometry. In the non-physical 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 log-evidence. Indeed, the Bianchi pattern is quite efficient at accounting for some of the large-scale 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 VIIh cosmology and constrain the vorticity of such models to (?/H)0<8.1 * 10-10 (95% confidence level).

KW - cosmology

KW - cosmic background radiation

KW - cosmological parameters

KW - gravitation

KW - data analysis

U2 - 10.1051/0004-6361/201321546

DO - 10.1051/0004-6361/201321546

M3 - Article

VL - 571

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

SN - 0004-6361

M1 - A26

ER -