1BeyondBigBangandPlanckscaleEightyyearsaftertheBigBanghypothesisformulatedbyGeorgesLema ID: 332082
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Noncyclicpre-BigBangLuisGonzalez-Mestres 1.BeyondBigBangandPlanckscaleEightyyearsaftertheBigBanghypothesisformulatedbyGeorgesLemaître[ 10 ],WMAPandPlanckmayallowtoexploretheoriginoftheUniverse,aswellasthestructureofmatterandspace-time,beyondtheprimevalquantahepostulated.Issueslikethepossiblelackofrandomnessofcosmicmicrowavebackground(CMB)[ 1 ]arerelevantnotonlyforconformalcycliccosmologies(CCC)[ 2 ].Theycanalsobecrucialforpre-BigBangpatternswithapossiblenewerabeforetheBigBang,newpropertiesofmatter[ 3 , 4 ]andanewspace-timestructure[ 7 , 8 ].Theseapproachesnaturallyleadtoalternatives[ 4 , 6 ]tostandardcosmology,ination,darkmatteranddarkenergy.Apre-BigBangscenariobasedonstringmodelsalsoexists[ 11 ],butstringscanresultfromanunderlyingcompositestructure[ 6 , 9 ]andnolongermakesensebelowsomedistancescale.Contrarytoearlymodelsthatusedpreonsasmerebuildingblockswithsimilarpropertiestothoseofstandardparticles,thesuperbradyonhypothesisproposedin1995[ 5 , 6 ]assumesthatthecriticalspeedcsofthenewpreonicconstituentsismuchlargerthanthespeedoflightc,justascisaboutamilliontimesthespeedofsound.Thephysicalvacuumisthenamaterialmediumul-timatelymadeoftheactualfundamentalmatter(thesuperbradyons),whereconventionalparticlescanexistasexcitationssimilartophonons,solitons...ThechoiceofaLorentzmetricforsuper-bradyonswithcsasthecriticalspeedappearsnatural,asotherspace-timemetricsareexpectedtoproducevacuuminstabilities[ 3 ].Theexistenceofapreferredreferenceframe(the"vacuumrestframe",VRF)isabasicandpermanentingredientofsuchnewphysicsandcosmology.Ifthevacuumismadeofsuperbradyonicmatter,standardgaugetheoriesandconventionalsymmetries(includingLorentzsymmetry)willprovideonlyasectoriallow-energylimit.TheHiggsbosonandthezeromodesofbosonicharmonicoscillatorsdonotneedtobepermanentlymaterializedinvacuum.Thecosmologicalconstantproblemmaythenbenaturallysolved.Quan-tumeldtheory,includingthecalculationofFeynmandiagrams,isexpectedtoundergomodi-cationsatveryhighenergy[ 3 , 4 ].QuantummechanicsandothercurrentlyadmittedprinciplesofPhysicswillnotnecessarilyholdbeyondthePlanckscaleorevenbeforereachingit[ 8 ].ItisusuallybelievedthatstandardsymmetriesofParticlePhysicsshouldlookmoreandmoreexactastheenergyscaleconsideredincreasesandmassescanbeneglected.Butitmayactuallyhappenthat,abovesometransitionenergybelowPlanckscale,thesituationchangesandtracksfromnewphysicsgeneratedatthePlanckscaleandbeyondbecomeincreasinglyimportant[ 8 , 12 ].IffreesuperbradyonscanexistinourUniversewithspeedslargerthanc,theywouldspon-taneouslyemit"Cherenkow"radiationintheformofstandardparticles.Remnantsuperbradyonswithaspeedclosetoccanthenformacosmologicalseaandanewdarkmattercomponent[ 4 , 8 ].Inthiscontext,twokindsofpre-BigBangscenarioscanbeconsidered:i)apre-Universemadeoftheactualultimateconstituentsofmatterandruledbytheirowndynamicallaws;ii)aninitialsingularityfollowedbyaprocessgeneratingthe"primevalquanta"[ 10 ]oftheBigBang.Theinitialsingularityinii)canactuallycorrespondtoanucleationinsidethepre-Universeofi).TheBigBangitselfcanbereplacedbyasuperbradyonera[ 6 , 9 ]withatransitiontostandardmatteratalowertemperature,thusprovidingadirectalternativetoination[ 6 , 13 ].Thespace-timegeometryiscrucialforthestudyofpre-BigBangpatternsandcanleadtounexpectedmodicationsofconventionalviewsconcerningtheoriginandevolutionofourUniverse.2 Noncyclicpre-BigBangLuisGonzalez-Mestres 2.Aspinorialspace-timeAsspin-1/2particlesexistinourUniverse,themostnaturaldescriptionofspace-timewouldbeaspinorialone[ 7 , 8 ]with,atleast,aSU(2)symmetrygroup[ 14 ].Withtheseminimalhypotheses,takingapreferredreferenceframeassuggestedbycosmologicaldataandrequiredifsuperbradyonsexist,acosmictimecanbedened.Givenaspinorx,andconsideringthepositiveSU(2)scalarjxj2=x†xwherethedaggerstandsforhermiticconjugate,thecosmictimewouldbet=jxjandtheassociatedspacegivenbytheS3hyperspherejxj=t.Then,ifx0istheobserverpositiononthejxj=t0hypersphere,spacetranslationscorrespondtoSU(2)transformationsactingonthespinorspace,i.e.x=Ux0whereU=exp(i=2t�10~s:~x)U(~x),and~sisthevectorformedbythePaulimatrices.Thevector~xisthespatialpositionofxwithrespecttox0atconstanttimet0,andisdifferentfromthespinorialpositionx�x0.SpacerotationsareobtainedasSU(2)transformationsactingonthespatialpositionvectorwithrespecttoaxedpointx0.Theoriginofourtimecanbeassociatedtothepointx=0.ThisleadstoanaturallyexpandingUniversewherecosmologicalcomovingframeswouldcorrespondtostraightlinescrossingtheoriginx=0.Suchageometryautomaticallyyieldsthewell-knownrelationbetweenrelativevelocitiesanddistancesatcosmicscaleforcomovingframes,usuallycalledHubble'slawbutactuallyrstfor-mulatedbyGeorgesLemaître[ 15 , 16 ].Inourspinorialapproachtospace-time,ifqisaconstantangulardistancebetweentwocosmologicalcomovingframes,theS3spatialdistancedbetweenthetwocorrespondingpointsonthejxj=thyperspherewillbed=qt.TheratiobetweenrelativevelocitiesanddistancesisthengivenbytheinverseoftheageoftheUniverse.Thisvalueisinreasonableagreementwithpresentobservationswhilematter,standardrelativity,gravitationandspecicspaceunitshavenotyetbeenintroducedinourdescriptionofspace-time.Itisthere-foretemptingtoconjecturethattheusuallypostulateddarkenergyisnotrequiredtoexplaintheobservedaccelerationoftheexpansionoftheUniverse.Instead,gravitationalandotherstandardeffectscanpossiblyaccountforpastuctuationsofthevelocity/distanceratio[ 8 , 9 ].Althoughthespinorialrelativepositionx�x0denedabovecorrespondstoapaththroughpasttimesviolatingstandardcausality,andtheproductionofhalf-integerorbitalangularmomentainexperimentshasneverbeenreported,itmayhappenthatsuchapositionspinormakessenseatverysmalldistancescales.Itwouldthenbepossibletogeneratethespin1/2asanactualinternalorbitalmomentuminanunderlyingcompositepictureofquarksandleptonspossiblylinkedtoapre-BigBangcosmology.Then,thespinorialspace-timewouldalsobecrucialforourunderstand-ingoftheultimatestructureofmatterbeyondconventionalquantumeldtheory.ContrarytotheconventionalmathematicalstructureofthePoincarégroup,thespinorialspace-timediscussedhereincorporatesspacetranslationsandrotationsinasinglecompactgroup.ThisisradicallydifferentfromtheassumptionsthatledtotheColeman-Madulatheoremin1967[ 17 ].Therefore,thepresentSU(2)approachtospace-timeanditsnaturalSL(2,C)extensioncanopenthewaytoanewunicationbetweenspace-timeandinternalsymmetries[ 8 ].Suchanewuniedsymmetrymayinturnprovideindirectchecksofthespinorialspace-timepatternsuggested.ThisSU(2)descriptionofspace-timeconsideredhereisalsoclosetoaSO(4)approachwhere,insteadofbeingimaginary,thecosmictimewouldbegivenbythemodulusofafour-vector[ 8 ].Todate,cosmologicaldatahavenotexcludedaS3hypersphericalUniverse.3