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1、TopologicalLensinginSphericalSpacesEveliseGausmann1,RolandLehoucq2,Jean-PierreLuminet1,Jean-PhilippeUzan3andJeffreyWeeks4(1)D´epartementd’AstrophysiqueRelativisteetdeCosmologie,ObservatoiredeParis–C.N.R.S.UMR8629,F-92195MeudonCedex(France).(2)CE-Saclay,DS
2、M/DAPNIA/Serviced’Astrophysique,F-91191GifsurYvetteCedex(France)(3)LaboratoiredePhysiqueTh´eorique–C.N.R.S.UMR8627,Bˆat.210,Universit´eParisXI,F-91405OrsayCedex(France).(4)15FarmerSt.,CantonNY13617-1120,USA.Abstract.Thisarticlegivestheconstructionandcomp
3、leteclassificationofallthree–dimensionalsphericalmanifolds,andordersthembydecreasingvolume,inthecontextofmulticonnecteduniversemodelswithpositivespatialcurvature.Itdiscusseswhichsphericaltopologiesarelikelytobedetectablebycrystallographicmethodsusingthree
4、–dimensionalcatalogsofcosmicobjects.Theexpectedformofthepairseparationhistogramispredicted(includingthelocationandheightofthespikes)andiscomparedtocomputersimulations,showingthatthismethodisstablewithrespecttoobservationaluncertaintiesandiswellsuitedford
5、etectingsphericaltopologies.PACSnumbers:98.80.-q,04.20.-q,02.40.Pc1.IntroductionThesearchforthetopologyofouruniversehasfocusedmainlyoncandidatespacetimeswithlocallyEuclideanorhyperbolicspatialsections.Thiswasmotivatedontheonehandbythemathematicalsimplici
6、tyofthree–dimensionalEuclideanmanifolds,andontheotherhandbyobservationaldatawhichhad,untilrecently,favoredalowdensityarXiv:gr-qc/0106033v111Jun2001universe.Morerecently,however,acombinationofastrophysicalandcosmologicalobservations(amongwhichtheluminosit
7、ydistance–redshiftrelationuptoz∼1fromtypeIasupernovae[1],thecosmicmicrowavebackground(CMB)temperatureanisotropies[2],gravitationallensing[3],velocityfields[4],andcomovingstandardrulers[5])seemstoindicatethattheexpansionoftheuniverseisaccelerating,withabou
8、t70%ofthetotalenergydensityΩ0beingintheformofadarkcomponentΩΛ0withnegativepressure,usuallyidentifiedwithacosmologicalconstanttermoraquintessencefield[6].Asaconsequence,thespatialsectionsoftheuniversewouldbe“almost”locallyflat
