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1、REVIEWSOFMODERNPHYSICS,VOLUME84,APRILJUNE2012TheoreticalaspectsofmassivegravityKurtHinterbichler*CenterforParticleCosmology,DepartmentofPhysicsandAstronomy,UniversityofPennsylvania,209South33rdStreet,Philadelphia,Pennsylvania19104,USA(published7May2012)Massivegravityhasseenaresurgenceofi
2、nterestduetorecentprogresswhichhasovercomeitstraditionalproblems,yieldinganavenueforaddressingimportantopenquestionssuchasthecosmologicalconstantnaturalnessproblem.Thepossibilityofamassivegravitonhasbeenstudiedonandoffforthepast70years.Duringthistime,curiositiessuchasthevanDam,Veltman,an
3、dZakharov(vDVZ)discontinuityandtheBoulware-Deserghostwereuncovered.TheseresultsarerederivedinapedagogicalmannerandtheStu¨ckelbergformalismtodiscussthemfromthemoderneffectivefieldtheoryviewpointisdeveloped.Recentprogressofthelastdecadeisreviewed,includingthedissolutionofthevDVZdiscontinuit
4、yviatheVainshteinscreeningmechanism,theexistenceofaconsistenteffectivefieldtheorywithastablehierarchybetweenthegravitonmassandthecutoff,andtheexistenceofparticularinteractionswhichraisethemaximaleffectivefieldtheorycutoffandremovetheghosts.Inaddition,somepeculiaritiesofmassivegravitonsoncu
5、rvedspace,noveltheoriesinthreedimensions,andexamplesoftheemergenceofamassivegravitonfromextradimensionsandbraneworldsarereviewed.DOI:10.1103/RevModPhys.84.671PACSnumbers:04.50.Kd,11.10.zCONTENTSB.TheappearanceofGalileonsandtheabsenceofghosts698C.The3Vainshteinradius699I.Introduction671
6、D.TheVainshteinmechanisminthe3theory700A.Generalrelativityismasslessspin2671E.Quantumcorrectionsinthe3theory700B.Modifyinggeneralrelativity673IX.BraneworldsandtheResonanceGraviton701C.Historyandoutline674A.TheDGPaction701II.TheFreeFierz-PauliAction675B.Linearexpansion703A.Hamiltonianan
7、ddegreeoffreedomcount675C.Resonancegravitons705B.Freesolutionsandgravitonmodefunctions676X.ConclusionsandFutureDirections706C.Propagator678Appendix:TotalDerivativeCombinations707III.LinearResponsetoSources679A.Generalsolutiontothesourcedequations680B.Solutionforapointsour
