Dark-Energy Dynamics Required to Solve the Cosmic

arXiv:0712.3099v1[astro-ph]19Dec2007Dark-EnergyDynamicsRequiredtoSolvetheCosmicCoincidenceChasA.EganDepartmentofAstrophysics,SchoolofPhysics,UniversityofNewSouthWales,Sydney,Australia∗CharlesH.LineweaverResearchSchoolofAstronomyandAstrophysics,AustralianNationalUniversity,Canberra,Australia†Dynamicdarkenergy(DDE)modelsareoftendesignedtosolvethecosmiccoincidence(why,justnow,isthedarkenergydensityρde,thesameorderofmagnitudeasthematterdensityρm?)byguaranteeingρde∼ρmforsignificantfractionsoftheageoftheuniverse.Thistypicallyentailsad-hoctrackingoroscillatorybehaviourinthemodel.However,suchbehaviourisneithersufficientnornecessarytosolvethecoincidenceproblem.Whatmustbeshownisthatasignificantfractionofobserversseeρde∼ρm.Preciselywhen,andforhowlong,mustaDDEmodelhaveρde∼ρminordertosolvethecoincidence?Weexplorethecoincidenceproblemindynamicdarkenergymodelsusingthetemporaldistributionofterrestrial-planet-boundobservers.Wefindthatanydarkenergymodelfittingcurrentobservationalconstraintsonρdeandtheequationofstateparametersw0andwa,doeshaveρde∼ρmforalargefractionofobserversintheuniverse.ThisdemotivatesDDEmodelsspecificallydesignedtosolvethecoincidenceusinglongorrepeatedperiodsofρde∼ρm.I.INTRODUCTIONIn1998,usingsupernovaeIaasstandardcandles,Riessetal.[1]andPerlmutteretal.[2]revealedarecentandcontinuingepochofcosmicacceleration-strongevidencethatEinstein’scosmologicalconstantΛ,orsomethingelsewithcomparablenegativepressurepde∼−ρde,cur-rentlydominatestheenergydensityoftheuniverse[3].Λisusuallyinterpretedastheenergyofzero-pointquan-tumfluctuationsinthevacuum[4,5]withaconstantequationofstatew≡pde/ρde=−1.Thisnecessaryad-ditionalenergycomponent,construedasΛorotherwise,hasbecomegenericallyknownas“darkenergy”(DE).Aplethoraofobservationshavebeenusedtoconstrainthefreeparametersofthenewstandardcosmologicalmodel,ΛCDM,inwhichΛdoesplaytheroleofthedarkenergy.Hinshawetal.[6]findthattheuniverseisex-pandingatarateofH0=71±4km/s/Mpc;thatitisspatiallyflatandthereforecriticallydense(Ωtot0=ρtot0ρcrit0=8πG3H20ρtot0=1.01±0.01);andthatthetotalden-sityiscomprisedofcontributionsfromvacuumenergy(ΩΛ0=0.74±0.02),colddarkmatter(CDM;ΩCDM0=0.22±0.02),baryonicmatter(Ωb0=0.044±0.003)andradiation(Ωr0=4.5±0.2×10−5).Henceforthwewillassumethattheuniverseisflat(Ωtot0=1)aspredictedbyinflationandsupportedbyobservations.Twoproblemshavebeeninfluentialinmouldingideasaboutdarkenergy,specificallyindrivinginterestinal-ternativestoΛCDM.Thefirstoftheseproblemsiscon-cernedwiththesmallnessofthedarkenergydensity∗VisitingtheResearchSchoolofAstronomyandAstro-physics,AustralianNationalUniversity;Electronicaddress:[e-mail]†PlanetaryScienceInstitute,AustralianNationalUniversity;Re-searchSchoolofEarthSciences,AustralianNationalUniversity[4,7,8].Despiterepresentingmorethan70%ofthetotalenergyoftheuniverse,thecurrentdarkenergydensityis∼120ordersofmagnitudesmallerthanenergyscalesattheendofinflation(or∼80ordersofmagnitudesmallerthanenergyscalesattheendofinflationifthisoccurredattheGUTratherthanPlanckscale)[7].Darkenergycandidatesarethuschallengedtoexplainwhytheob-servedDEdensityissosmall.Thestandardidea,thatthedarkenergyistheenergyofzero-pointquantumfluc-tuationsinthetruevacuum,seemstooffernosolutiontothisproblem.Thesecondcosmologicalconstantproblem[9,10,11]isconcernedwiththenearcoincidencebetweenthecurrentcosmologicalmatterdensity(ρm0≈0.26×ρcrit0)andthedarkenergydensity(ρde0≈0.74×ρcrit0).InthestandardΛCDMmodel,thecosmologicalwindowduringwhichthesecomponentshavecomparabledensityisshort(just1.5e-foldsofthecosmologicalscalefactora)sincematterdensitydilutesasρm∝a−3whilevacuumdensityρdeisconstant[12].Thus,evenifoneexplainswhytheDEdensityismuchlessthanthePlanckdensity(thesmallnessproblem)onemustexplainwhywehappentoliveduringthetimewhenρde∼ρm.Toquantifythetime-dependentproximityofρmandρde,wedefineaproximityparameter,r≡minρdeρm,ρmρde,(1)whichrangesfromr≈0,whenmanyordersofmagni-tudeseparatethetwodensities,tor=1,whenthetwodensitiesareequal.Thepresentlyobservedvalueofthisparameterisr0=ρm0ρde0≈0.35.Intermsofr,thecoinci-denceproblemisasfollows.IfwenaivelypresumethatthetimeofourobservationtobshasbeendrawnfromadistributionoftimesPt(t)spanningmanydecadesofcosmicscalefactor,wefindthattheexpectedproximityparameterisr≈0≪0.35.InthetoppanelofFig.1we2useanaivedistributionfortobsthatisconstantinlog(a)toillustratehowobservingraslargeasr0≈0.35seemsunexpected.InLineweaverandEgan[12]weshowedhowtheappar-entseverityofthecoincidenceproblemstronglydependsuponthedistributionPt(t)fromwhichtobsishypoth-esizedtohavebeendrawn.Naivepriorsfortobs,suchastheoneillustratedinthetoppanelofFig.1,leadtonaiveconclusions.However,thecoincidenceproblemcanbemoremeaningfullyquantifiedwhenthenecessaryconstraintthattobshasbeendrawnfromthetemporaldistributionofobserversisincluded.Thetemporalandspatialdistributionofobservershasbeenestimatedus-inglarge(1011M⊙)galaxies[13,14,15]andterrestrialplanets[12]astracers.ThetoppanelofFig.1showsthetemporaldistributionofobserversPt(t)fromLineweaverandEgan[12].InLineweaverandEgan[12]weassessedtheseverityofthecoinci