CMB anisotropy of the Poincaré dodecahedron

Aurich, R.; Lustig, Sven; Steiner, Frank

doi:10.1088/0264-9381/22/11/010

Cited by 75 publications

(170 citation statements)

References 62 publications

(159 reference statements)

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“…With data from the WMAP satellite (Jarosik et al 2011), these theoretical and observational tools were applied to a high-quality dataset for the first time. Luminet et al (2003) and Caillerie et al (2007) claimed the low value of the low multipoles (compared to standard ΛCDM cosmology) as evidence for missing large-scale power as predicted in a closed universe with a small fundamental domain (see also Aurich 1999;Aurich et al 2004Aurich et al , 2005Aurich et al , 2006Aurich et al , 2008Aurich & Lustig 2013;Lew & Roukema 2008;Roukema et al 2008). However, searches in pixel space (Cornish et al 2004;Key et al 2007;Niarchou et al 2004;Bielewicz & Riazuelo 2009;Dineen et al 2005) and in harmonic space (Kunz et al 2006) determined that this was an unlikely explanation for the low power.…”

Section: Previous Resultsmentioning

confidence: 96%

Planck2013 results. XXVI. Background geometry and topology of the Universe

Ade¹,

Aghanim²,

Arnaud³

et al. 2014

A&A

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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 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), 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 R i 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, 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 back-to-back circles, among them tori and the three spherical cases listed above, coming from the matched-circles 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 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 simultaneousl...

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Section: Previous Resultsmentioning

confidence: 96%

Planck2013 results. XXVI. Background geometry and topology of the Universe

Ade¹,

Aghanim²,

Arnaud³

et al. 2014

A&A

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“…In the following, we again take into account the Planck constraints on the cosmological density parameters [1] that permit χ LSS = 0.038, and present concrete examples (with smaller values for p) of nearly flat universes with lens-space spatial topology that give rise to detectable circles-in-the-sky in which either values of the observable parameters λ (radius of circles) or θ (deviation from antipodality), or even both values, fall outside the ranges covered by the searches so far undertaken [6][7][8][9][10][11][12][13]17].…”

Section: Concrete Examplesmentioning

confidence: 99%

“…Although in all universes of Table I both the radii of the circles, λ, and the deviation from antipodality, θ, fall outside the ranges covered by the searches carried out so • TABLE I: Globally inhomogeneous lens spaces L(p, q) spatial topology of nearly flat universes with χ LSS = 0.038, for which both the maximal deviation of antipodality, θ max , and the radius of the matching circles, λ, fall outside the range covered in the searches carried out with either WMAP or Planck data [6][7][8][9][10][11][12][13]17]. As explained in Appendix G, q ⊥ is the least value of q for which θ max > 170…”

Section: Concrete Examplesmentioning

confidence: 99%

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Limits of the circles-in-the-sky searches in the determination of cosmic topology of nearly flat universes

2016

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An important observable signature of a detectable nontrivial spatial topology of the Universe is the presence in the cosmic microwave background sky of pairs of matching circles with the same distributions of temperature fluctuations -the so-called circles-in-the-sky. Most of the recent attempts to find these circles, including the ones undertaken by the Planck Collaboration, were restricted to antipodal or nearly antipodal circles with radii λ ≥ 15• . In the most general search, pairs of circles with deviation from antipodality angles 0• ≤ θ ≤ 169• and radii 10 • ≤ λ ≤ 90• were investigated. No statistically significant pairs of matching circles were found in the searches so far undertaken. Assuming that the negative result of general search can be confirmed through analysis made with data from Planck and future cosmic microwave background (CMB) experiments, we examine the question as to whether there are nearly flat universes with compact topology, satisfying Planck constraints on cosmological parameters, that would give rise to circles-in-the-sky whose observable parameters λ and θ fall outside the parameter ranges covered by this general search. We derive the expressions for the deviation from antipodality and for the radius of the circles associated to a pair of elements (γ ,γ −1 ) of the holonomy group Γ which define the spatial section of any positively curved universe with a nontrivial compact topology. We show that there is a critical position that maximizes the deviation from antipodality, and prove that no matter how nearly flat the Universe is, it can always have a nontrivial spatial topology that gives rise to circles whose deviation from antipodality θ is larger than 169• , and whose radii of the circles λ are smaller than 10• for some observers's positions. This makes it apparent that slightly positively curved nearly flat universes with cosmological parameters within Planck bounds can be endowed with a nontrivial spatial topology with values of the observable parameters λ and θ outside the ranges covered by the searches for circles carried out so far with either WMAP or Planck data. Thus, these circles-inthe-sky searches carried out so far are not sufficient to exclude the possibility of a universe with a detectable nontrivial cosmic topology. We present concrete examples of lens spaces universes whose associated circles have both, or at least one value of the observable parameters (λ, θ) outside the ranges covered by these searches. We also present a brief discussion of the implications of our results in view of unavoidable practical limits of the circles-in-the-sky method. 98.80.Es, 98.80.Jk

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“…On the other hand, there are some reasons why the universe may have positive spatially a e-mail: aliakbar.asgari@modares.ac.ir b e-mail: ahabbasi@modares.ac.ir c e-mail: j.gholizadeh@modares.ac.ir curvature with non-trivial topology. In other words, some positive curvature models with non-trivial topology can solve the problem of the CMB quadrupole and octopole suppression and also the mystery of the missing fluctuations which appears in the concordance model of cosmology [14][15][16][17][18]. So these reasons augment the probability of a spatially closed case and it seems necessary to investigate the theory of small fluctuations in spatially closed universes.…”

Section: Introductionmentioning

confidence: 99%

On the perturbation theory in spatially closed background

2014

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In this article, we investigate some features of the perturbation theory in a spatially closed universe. We will show that the perturbative field equations in a spatially closed universe always have two independent adiabatic solutions provided that the wavelengths of perturbation modes are very much longer than the Hubble horizon. It will be revealed that these adiabatic solutions do not depend on the curvature directly. We also propose a new interpretation for the curvature perturbation in terms of the unperturbed background geometry.

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CMB anisotropy of the Poincaré dodecahedron

Cited by 75 publications

References 62 publications

Planck2013 results. XXVI. Background geometry and topology of the Universe

Planck2013 results. XXVI. Background geometry and topology of the Universe

Limits of the circles-in-the-sky searches in the determination of cosmic topology of nearly flat universes

On the perturbation theory in spatially closed background

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