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Ade, P.A.R. and Aghanim, N. and Arnaud, M. and Ashdown, M. and Aumont, J. and Baccigalupi, C. and Banday, A.J. and Barreiro, R.B. and Bartolo, N. and Basak, S. and Battaner, E. and Benabed, K. and Benoît, A. and Benoit-Lévy, A. and Bernard, J.-P. and Bersanelli, M. and Bielewicz, P. and Bock, J.J. and Bonaldi, A. and Bonavera, L. and Bond, J.R. and Borrill, J. and Bouchet, F.R. and Bucher, M. and Burigana, C. and Butler, R.C. and Calabrese, E. and Cardoso, J.-F. and Catalano, A. and Challinor, A. and Chamballu, A. and Chiang, H.C. and Christensen, P.R. and Church, S. and Clements, D.L. and Colombi, S. and Colombo, L.P.L. and Combet, C. 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 Désert, F.-X. and Diego, J.M. and Dole, H. and Donzelli, S. and Doré, O. and Douspis, M. and Ducout, A. and Dupac, X. and Efstathiou, G. and Elsner, F. and Enßlin, T.A. and Eriksen, H.K. and Feeney, S. and Fergusson, J. and Finelli, F. and Forni, O. and Frailis, M. and Fraisse, A.A. and Franceschi, E. and Frejsel, A. and Galeotta, S. and Galli, S. and Ganga, K. and Giard, M. and Giraud-Héraud, Y. and Gjerløw, E. and González-Nuevo, J. and Górski, K.M. and Gratton, S. and Gregorio, A. and Gruppuso, A. and Gudmundsson, J.E. and Hansen, F.K. and Hanson, D. and Harrison, D.L. and Henrot-Versillé, S. and Hernández-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 Hurier, G. and Jaffe, A.H. and Jaffe, T.R. and Jones, W.C. and Juvela, M. and Keihänen, E. and Keskitalo, R. and Kisner, T.S. and Knoche, J. and Kunz, M. and Kurki-Suonio, H. and Lagache, G. and Lähteenmäki, A. and Lamarre, J.-M. and Lasenby, A. and Lattanzi, M. and Lawrence, C.R. and Leonardi, R. and Lesgourgues, J. and Levrier, F. and Liguori, M. and Lilje, P.B. and Linden-Vørnle, M. and López-Caniego, M. and Lubin, P.M. and Macías-Pérez, J.F. and Maggio, G. and Maino, D. and Mandolesi, N. and Mangilli, A. and Maris, M. and Martin, P.G. and Martínez-González, E. and Masi, S. and Matarrese, S. and McEwen, J.D. and McGehee, P. and Meinhold, P.R. and Melchiorri, A. and Mendes, L. and Mennella, A. and Migliaccio, M. and Mitra, S. and Miville-Deschênes, M.-A. and Moneti, A. and Montier, L. and Morgante, G. and Mortlock, D. and Moss, Adam and Munshi, D. and Murphy, J.A. and Naselsky, P. and Nati, F. and Natoli, P. and Netterfield, C.B. and Nørgaard-Nielsen, H.U. and Noviello, F. and Novikov, D. and Novikov, I. 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.V. and Perdereau, O. and Perotto, L. and Perrotta, F. and Pettorino, V. 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 Popa, L. and Pratt, G. W. and Prézeau, 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 Renzi, A. and Ristorcelli, I. and Rocha, G. and Rosset, C. and Rossetti, M. and Roudier, G. and Rowan-Robinson, M. and Rubiño-Martín, J. A. and Rusholme, B. and Sandri, M. and Santos, D. and Savelainen, M. and Savini, G. and Scott, D. and Seiffert, M.D. and Shellard, E.P.S. and Spencer, L.D. and Stolyarov, V. and Stompor, R. and Sudiwala, R. and Sutton, D. and Suur-Uski, A.-S. and Sygnet, J.-F. and Tauber, J.A. 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, F. and Vielva, P. and Villa, F. and Wade, L.A. and Wandelt, B.D. and Wehus, I.K. and Yvon, D. and Zacchei, A. and Zonca, A. (2016) Planck 2015 results. XVIII. Background geometry and topology of the Universe. Astronomy & Astrophysics, 594 . A18/1-A18/21. ISSN 1432-0746

Abstract

Maps of cosmic microwave background (CMB) temperature and polarization from the 2015 release of Planck data provide the highestquality full-sky 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 non-trivial topology with a fundamental domain that intersects, or nearly intersects, the last-scattering surface (at comoving distance χrec), 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 last-scattering surface. The limits on the radius ℛi of the largest sphere inscribed in the fundamental domain (at log-likelihood ratio Δlnℒ > −5 relative to a simply-connected flat Planck best-fit model) are: ℛi > 0.97 χrec for the T3 cubic torus; and ℛi > 0.56 χrec for the T1 slab. The limit for the T3 cubic torus from the matched-circles search is numerically equivalent, ℛi > 0.97 χrec at 99% confidence level from polarization data alone. 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 temperature data favour the inclusion of a Bianchi component with a Bayes factor of at least 2.3 units of log-evidence. 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 VIIh cosmology and constrain the vorticity of such models to (ω/H)0 < 7.6 × 10-10 (95% CL).

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