(ppt) introduction to brane inflation (horace stoica)(october 31, 2007)

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1、IntroductiontoBraneInflationHoraceStoicaOctober31,2007HoraceStoicaIntroductiontoBraneInflationOutlineIBriefintroductiontoCosmology/InflationIStringTheoryandtheBraneworldIBraneInflationITopologicalDefectsIInputfromObservations:PresentandFutureExperimentsIFutureDirectio

2、nsandConclusionsHoraceStoicaIntroductiontoBraneInflationThescaleofEnergies:WhatweknowandwhatwebelieveIIfwewanttohaveacompletetheorywewillneedtoknowthephysicsatallenergyscales.IHowdoweexplorephysicsattheGUTscale?HoraceStoicaIntroductiontoBraneInflationMilestonesinthe

3、EvolutionoftheUniversehttp://map.gsfc.nasa.gov/mmm.htmlHoraceStoicaIntroductiontoBraneInflationShortIntroductiontoCosmologyTheFriedman-Robertson-WalkermetricforahomogeneousandisotropicUniverse:dr2
ds2=−dt2+a2(t)+r2dθ2+sin2θdφ21−κr2
=−dt2+a2(t)d`2+r2(`)dθ2+sin

4、2θdφ2Fromthedefinitiond`=dr/(1−κr2)1/2onegets:sin`ifκ=+1r(`)=`ifκ=0sinh`ifκ=−1IForκ=1thespatialslicesare3-spheres,closedUniverse.IForκ=−1hyperbolicsurfaces,openUniverse.HoraceStoicaIntroductiontoBraneInflationTheEinsteinEquationsZ√R1S=−dtd3x−g+∂φ∂µφ+V(φ)16

5、πG2µ

6、{z}LmatterVaryingtheactionwithrespecttogµνweobtaintheEinsteinequations:1Rµν−Rgµν=8πGTµν2wherethestress-energytensoris:2∂SmatterTµν=√−g∂gµνItislocallyconserved:∇µT=0µνHoraceStoicaIntroductiontoBraneInflationStressEnergyTensor:PerfectFluidThemostgeneralformofgµ

7、νconsistentwithahomogeneousandisotropicuniverseis:ρ0Tµν=0pgijTheEinsteinandstress-energyconservationequations:2a˙κ8πG+=ρ(0,0)componentaa23¨a4πG=−(ρ+3p)(i,i)componenta3(a3˙ρ)+p(a˙3)=0energyconservationForthemostcommontypesofmatterp=wp:a˙ρ˙+3(1+w)ρ=0aHoraceStoic

8、aIntroductiontoBraneInflationTypesofMatterThevarioustypesofmatterarecharacterizedbythevalueofw.IDustorDarkMatter:w=0.a˙ρ0ρ˙+3ρ=0→ρ=aa3IRadiation:w=1/3.a˙ρ0ρ˙+4ρ=0→ρ=aa4IDarkEnergy:w=−1.ρ˙=0→ρ=ρ0=constantThemostgeneralFRWuniverseevolveslike:2hi2a˙κ8πGρmρrH=+=ρΛ++a

9、a23a3a4HoraceStoicaIntroductiontoBraneInflationEvolutiondependenceontheEnergyDominationDependingonthedominantenergycomponent,theuniverseexpandslike:2a(t)