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    Planck 2013 results. XXVI. Background geometry and topology of the Universe

    Ade, P.A.R. and Aghanim, N. and Armitage-Caplan, C. and Arnaud, M. and Ashdown, M. and Atrio-Barandela, F. and Aumont, J. and Baccigalupi, C. and Banday, A.J. and Barreiro, R.B. and Bartlett, J.G. and Battaner, E. and Benabed, K. and Benoit, A. and Benoit-Lévy, A. and Bernard, J.-P. and Bersanelli, M. and Bielewicz, P. and Bobin, J. and Bock, J.J. and Bonaldi, A. and Bonavera, L. and Bond, J.R. and Borrill, J. and Bouchet, F.R. and Bridges, M. and Bucher, M. and Burigana, C. and Butler, R.C. and Cardoso, J.-F. and Catalano, A. and Challinor, A. and Chamballu, A. and Chiang, H.C. and Chiang, L.-Y. and Christensen, P.R. and Church, S. and Clements, D.L. and Colombi, S. and Colombo, L.P.L. and Couchot, F. and Coulais, A. and Crill, B.P. and Curto, A. and Cuttaia, F. and Danese, L. and Davies, R.D. and Davis, R.J. and De Bernardis, P. and de Rosa, A. and de Zotti, G. and Delabrouille, J. and Delouis, J.-M. and Desert, F.-X. and Diego, J.M. and Dole, H. and Donzelli, S. and Dore, O. and Douspis, M. and Dupac, X. and Efstathiou, G. and Enßlin, T.A. and Eriksen, H.K. and Fabre, O. and Finelli, F. and Forni, O. and Frailis, M. and Franceschi, E. and Galeotta, S. and Ganga, K. and Giard, M. and Giardino, G. and Giraud-Héraud, Y. and Gonzalez-Nuevo, J. and Gorski, K.M. and Gratton, S. and Gregorio, A. and Gruppuso, A. and Hansen, F.K. and Hanson, D. and Harrison, D. and Henrot-Versille, S. and Hernandez-Monteagudo, C. and Herranz, D. and Hildebrandt, S.R. and Hivon, E. and Hobson, M. and Holmes, W.A. and Hornstrup, A. and Hovest, W. and Huffenberger, K.M. and Jaffe, A.H. and Jaffe, T.R. and Jones, W.C. and Juvela, M. and Keihanen, E. and Keskitalo, R. and Kisner, T.S. and Knoche, J. and Knox, L. and Kunz, M. and Kurki-Suonio, H. and Lagache, G. and Lahteenmaki, A. and Lamarre, J.-M. and Lasenby, A. and Laureijs, R.J. and Lawrence, C.R. and Leahy, J.P. and Leonardi, R. and Leroy, C. and Lesgourgues, J. and Liguori, M. and Lilje, P.B. and Linden-Vornle, M. and Lopez-Caniego, M. and Lubin, P.M. and Macias-Perez, J.F. and Maffei, B. and Maino, D. and Mandolesi, N. and Maris, M. and Marshall, D.J. and Martin, P.G. and Martinez-Gonzalez, E. and Masi, S. and Massardi, M. and Matarrese, S. and Matthai, F. and Mazzotta, P. and McEwen, J.D. and Melchiorri, A. and Mendes, L. and Mennella, A. and Migliaccio, M. and Mitra, S. and Miville-Deschenes, M.-A. and Moneti, A. and Montier, L. and Morgante, G. and Mortlock, D. and Moss, A. and Munshi, D. and Murphy, J.Anthony and Naselsky, P. and Nati, F. and Natoli, P. and Netterfield, C.B. and Norgaard-Nielsen, H.U. and Norgaard-Nielsen, H.U. and Noviello, F. and Novikov, D. and Novikov, I. and Osborne, S. and Oxborrow, C.A. and Paci, F. and Pagano, L. and Pajot, F. and Paoletti, D. and Pasian, F. and Patanchon, G. and Peiris, H. and Perdereau, O. and Perotto, L. and Perrotta, F. and Piacentini, F. and Piat, M. and Pierpaoli, E. and Pietrobon, D. and Plaszczynski, S. and Pogosyan, D. and Pointecouteau, E. and Polenta, G. and Ponthieu, N. and Popa, L. and Poutanen, T. and Pratt, G.W. and Prezeau, G. and Prunet, S. and Puget, J.-L. and Rachen, J.P. and Rebolo, R. and Reinecke, M. and Remazeilles, M. and Renault, C. and Riazuelo, A. and Ricciardi, S. and Riller, T. and Ristorcelli, I. and Rocha, G. and Rosset, C. and Roudier, G. and Rowan-Robinson, M. and Rusholme, B. and Sandri, M. and Santos, D. and Savini, G. and Scott, D. and Seiffert, M.D. and Shellard, E.P.S. and Spencer, L. and Starck, J.-L. and Stolyarov, V. and Stompor, R. and Sudiwala, R. and Sureau, F. and Sutton, D. and Suur-Uski, A.-S. and Sygnet, J.-F. and Tauber, J.A. and Tavagnacco, D. and Terenzi, L. and Toffolatti, L. and Tomasi, M. and Tristram, M. and Tucci, M. and Tuovinen, J. and Valenziano, L. and Valiviita, J. and Van Tent, B. and Varis, J. and Vielva, P. and Villa, F. and Vittorio, N. and Wade, L.A. and Wandelt, B.D. and Yvon, D. and Zacchei, A. and Zonca, A. (2014) Planck 2013 results. XXVI. Background geometry and topology of the Universe. Astronomy & Astrophysics, 571 (A26). ISSN 0004-6361

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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 χrec), 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 Δln ℒ > −5 relative to a simply-connected flat Planck best-fit model) are: in a flat Universe, ℛi> 0.92χrec for the T3 cubic torus; ℛi> 0.71χrec for the T2 chimney; ℛi> 0.50χrec for the T1 slab; and in a positively curved Universe, ℛi> 1.03χrec for the dodecahedral space; ℛi> 1.0χrec for the truncated cube; and ℛi> 0.89χrec 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> 0.94χrec 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 (ω/H)0< 8.1 × 10-10 (95% confidence level).

    Item Type: Article
    Keywords: Planck Collaboration; cosmology: observations; cosmic background radiation; cosmological parameters; gravitation; methods: data analysis; methods: statistical;
    Academic Unit: Faculty of Science and Engineering > Experimental Physics
    Item ID: 14164
    Identification Number:
    Depositing User: Dr. Anthony Murphy
    Date Deposited: 10 Mar 2021 16:58
    Journal or Publication Title: Astronomy & Astrophysics
    Publisher: EDP Sciences
    Refereed: Yes

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