Noncommutative Conformally Coupled Scalar Field Cosmology an

We study the implications of a noncommutative geometry of the minisuperspace variables for the FRW universe with a conformally coupled scalar field. The investigation is carried out by means of a comparative study of the universe evolution in four differen

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002 tcO 72 2v170804/0ht-pe:hviXraNoncommutativeConformallyCoupledScalarFieldCosmologyandits

CommutativeCounterpart

G.D.Barbosa

CentroBrasileirodePesquisasF´ sicas,CBPF,

RuaDr.XavierSigaud150,22290-180,RiodeJaneiro,Brazil

WestudytheimplicationsofanoncommutativegeometryoftheminisuperspacevariablesfortheFRWuniversewithaconformallycoupledscalar eld.Theinvestigationiscarriedoutbymeansofacomparativestudyoftheuniverseevolutioninfourdi erentscenarios:classicalcommutative,classicalnoncommutative,quantumcommutative,andquantumnoncommutative,thelasttwoem-ployingtheBohmianformalismofquantumtrajectories.Theroleofnoncommutativityisdiscussedbydrawingaparallelbetweenitsrealizationsintwopossibleframeworksforphysicalinterpretation:theNC-frame,whereitismanifestintheuniversedegreesoffreedom,andintheC-frame,whereitismanifestthroughθ-dependenttermsintheHamiltonian.Asaresultofourcomparativeanalysis,we ndthatnoncommutativegeometrycanremovesingularitiesintheclassicalcontextforsu cientlylargevaluesofθ.Moreover,underspecialconditions,theclassicalnoncommutativemodelcanadmitbouncingsolutionscharacteristicofthecommutativequantumFRWuniverse.Inthequantumcon-text,we ndnon-singularuniversesolutionscontainingbouncesorbeingperiodicinthequantumcommutativemodel.Whennoncommutativitye ectsareturnedoninthequantumscenario,theycanintroducesigni cantmodi cationsthatchangethesingularbehavioroftheuniversesolutionsorthatrenderthemdynamicalwhenevertheyarestaticinthecommutativecase.Thee ectsofnoncommutativityarecompletelyspeci edonlywhenoneoftheframesforitsrealizationisadoptedasthephysicalone.Non-singularsolutionsintheNC-framecanbemappedintosingularonesintheC-frame.

PACSnumbers:98.80.Qc,04.60.Kz,11.10.Nx,11.10.Lm

I.INTRODUCTION

Overthelatestyearsagreatdealofworkande orthasbeendoneinthedirectionofunderstandingcanonicalnoncommutative eldtheoriesandquantummechanics(see[1,2]andreferencestherein).Therecentinterestinthesetheoriesismotivatedbyworksthatestablishaconnectionbetweennoncommutativegeometryandstringtheory[3].Intensiveresearchiscarriedouttoinvestigatetheirinterestingproperties,suchastheIR-UVmixingandnonlocality[4],Lorentzviolation[5],newphysicsatveryshortdistances[1,2],andtheequivalencebetweentranslationsinthenoncommutativedirectionsandgaugetransformations(see,e.g.[2,6]).

Severalinvestigationshavebeenpursuedtoverifythepossibleroleofnoncommutativityinagreatdealofcosmologicalscenarios.AmongthemwequoteNewtoniancosmology[7],cosmologicalperturbationtheoryandin ationarycosmology[8],noncommutativegravity[9],andquantumcosmology[10,11].Inapreviouswork[11],aninvestigationintothein uenceofnoncommutativityoftheminisuperspacevariablesintheearlyuniversescenariowascarriedoutfortheKantowski-Sachsuniverse.Althoughnoncommutativitye ectsprovedtoberelevanttotheuniversehistoryatintermediatetimes,theywereshownnottobecapableofremovingthefutureandpastcosmologicalsingularitiesofthatmodelintheclassicalcontext.Inthequantumcontext,ontheotherhand,non-singularuniversesolutionswereshowntobepresent.However,sincetheyexistforthecommutativequantumKantowski-Sachsuniverse,theirpresenceintheensembleofsolutionsofthenoncommutativequantummodelcannotbeattributedtothenoncommutativitye ects.

Althoughtheinvestigationcarriedoutin[11]wasrestrictedtoaparticularmodel,oneexpectedthatsomeoftheresultsobtainedtherecouldbeofgeneralvalidity.Indeed,inthisworkweshallshowthat

noncommutativity

We study the implications of a noncommutative geometry of the minisuperspace variables for the FRW universe with a conformally coupled scalar field. The investigation is carried out by means of a comparative study of the universe evolution in four differen

canappreciablymodifytheevolutionoftheFriedman-Robertson-Walker(FRW)universewithaconformallycoupledscalar eld[12,13].Asinreference[11],ourinvestigationiscarriedoutbymeansofacomparativestudyoftheuniverseevolutioninfourdi erentscenarios:classicalcommutative,classicalnoncommutative,quantumcommutativeandquantumnoncommutative.Themainmotivationforthechoiceoftheconformallycoupledscalar eldisthatitadmitsexactsolutionsinthesimplercasesdiscussedalongthisworkanditisrichenoughtobeusefulasaprobeforthesigni cantmodi cationsnoncommutativegeometryintroducesinclassicalandquantumcosmologies.Theanalyticaltreatmentrenderseasythestudyofthesingularbehaviorofthemodelinitsfourversions.Asweshallshowlater,evenintheclassicalcontextnoncommutativegeometrycanremovesingularities.Moreover,dependingonthevalueofthenoncommutativeparameter,noncommutativeclassicalmodelscanmimicquantume ects.

Asaninterpretationforquantumtheory,weareadoptingtheBohmianone,whichwebrie yreviewinsection4.OriginallyproposedbyBohmin1952[14],andfurtherdevelopedbyhiminacollaborationwithHiley[15],suchaninterpretationofquantumtheoryhasacquiredanincreasingnumberofadeptsalongtheyears[16].DecisivecontributionsforthedevelopmentoftheBohmianquantumphysicsweremadebyBell[17],whowasitsarduousdefenderforthreedecades,byHolland[18],andbyD.D¨urr,S.GoldsteinandN.Zangh` (see,e.g.,[19]-[22]andref.therein).Duetothecapabilityithastoreproducetheexperimentalresultsofquantummechanicsandquantum eldtheoryprovidinganintuitiveinterpretationoftheunderlyingdynamics,Bohmianquantumphysicsispresentlyanissueofinterestforbroadcommunity(see,e.g.,[23]).InthisworkthemainreasonthatcompelsustoadopttheBohmianinterpretationinquantumcosmologyistheabsenceofexternalobserversintheprimordialquantumuniverse,whichrendersthestandardCopenhageninterpretationinapplicableinitsdescription.Asanalternative,theBohmianinterpretationhasbeenemployedinseveralworksofquantumcosmologyandquantumgravity(see,e.g.,[11,13,24]).OtherinterestingaspectoftheBohmianapproachtoquantumtheory,whichmotivatesusfori …… 此处隐藏：5850字，全部文档内容请下载后查看。喜欢就下载吧 ……