Presentation on theme: "DGP gravity Theory and Phenomenology"— Presentation transcript:
1 DGP gravity Theory and Phenomenology Cédric Deffayet(APC & IAP, Paris)DGP gravityTheory andPhenomenologyFrom quantum to CosmosFundamental PhysicsResearch in SpaceQ2C Warrenton 20061/ DGP model (in 5D) or « brane induced gravity »2/ Cosmology and phenomenology
2 Why being interested in this model ? One way to modify gravity at « large distances »… and get rid of dark energy ?Changing the dynamics of gravity ?Dark matter or dark energy ?Historical example thesuccess/failure of bothapproaches: Le Verrier andThe discovery of NeptuneThe non discovery of Vulcan…but that of General Relativity
3 1. The DGP model (or brane-induced gravity). Dvali, Gabadadze, Porrati, 2000A « brane world » model: our 4D space-time is a surface embedded in a large space-timeStandard model5D Minkowskibulk space-timeSpecial equations of motion for gravity5D Einstein tensorBrane localizationIf equal to zero, standard, 4D, Einstein equations (~ = c =1)
4 Action principle for this Standard modelAction principle for thisUsual 5D brane world actionPeculiar toDGP modelBrane localized kineticterm for the gravitonWill generically be inducedby quantum correctionsA special hierarchy betweenM(5) and MP is requiredto render the modelphenomenologically interesting
5 DGP modelPhenomenological interestA new way to modify gravity at large distance, with a new type of phenomenology … (Important to have such models, if only to disentangle what does and does not depend on the large distance dynamics of gravity in what we know about the Universe)Theoretical interestConsistent (?) non linear massive gravity …
6 How does that work ? A scalar toy model for DGP 5D D’AlembertianSource for 4D D’AlembertianFor a localized static source, one find the following response5D potential at large distances4D potential at small distancesTransition
7 Newtonian potential on the brane behaves as Back to the DGP model :Newtonian potential on the brane behaves as4D behavior at small distances5D behavior at large distancesThe crossover distance between the two regimes is given byThis enables to get a “4D looking” theory of gravity out of one which is not, without having to assume a compact (Kaluza-Klein) or “curved” (Randall-Sundrum) bulk.But the tensorial structure of the graviton propagator is that of a massive graviton (gravity is mediated by a continuum of massive modes)Leads to the van Dam-Veltman-Zakharov discontinuity on Minkowski background!
8 This coefficient equals +1 in Schwarschild solution + … The vDVZ discontinuity as seen in Schwarzschild-type solution of « massive gravity » (DGP model, see thereafter!)+ …This coefficient equals +1 in Schwarschild solution+ …Vainshtein ‘72Wrong light bending!Introduces a new length scale r in the problem below which the perturbation theory diverges!VFor the sun: bigger than solar system!
9 So, what is going on at smaller distances? Vainshtein’s answer (1972):There exists an other perturbative expansion at smaller distances, reading:withThis goes smoothly toward Schwarschild as m goes to zeroNo warranty that this solution can be matched with the other for large r!Boulware, Deser ‘72
10 2. Phenomenology of DGP model 2.1 homogeneous cosmology a(t0)a(t)The dynamics of the scale factor a(t) of our 4D Universe (the brane) is governed by the modified Friedmann equationWithC.D. ‘01Analogous to standard (4D) Friedmann equationsfor small Hubble radiiEarly cosmology as usual
11 Late time deviation from standard cosmology Late time cosmologyDepending on the sign ofSelf accelerating solution (asympotes de Sitter space even with zero matter energy density)One virtue of DGP model: can get accelerated universe by large distance modification of gravity(C.D (‘01); C.D., Dvali, Gabadaze (‘02)).Brane cosmology in 5D Minkowski bulk with no R term on the brane (i.e.: solution to 5D Einstein-Hilbert Action)Late time deviation from standard cosmology
12 DGP self accelerating phase The brane (first) Friedmann equationCan be rewritten asPhase diagramwith = +1Maartens, MajerottoActs as a cosmological constant if = +1withSame number of parameter as CDM
13 Strictly speaking, only SN observations are depending solely on the background evolutions Vs. CDMMaartens, Majerotto ‘06DGPCMB and more importantly Baryon oscillations should be re-computed taking into account the peculiarities of DGP gravity
14 2. 2 Back to the van Dam-Veltman-Zakharov discontinuity… Exact cosmological solutions provide an explicit example of interpolation between theories with different tensor structure for the graviton propagator.C.D.,Gabadadze, Dvali, Vainshtein (2002)large rcsmall rcSolution of 4D GR with cosmic fluidSolution of 5D GR with a brane sourceComes in support of a « Vainshtein mechanism » [non perturbative recovery of the « massless » solutions] at work in DGP…… Recently an other exact solution found by Kaloper for localized relativistic source showing the same recovery…..
15 Related to strong self interaction of the brane bending sector Perturbative study of Schwarzschild type solutions of DGP model on a flat background space-time:Gruzinov, Porrati, Lue, Lue & Starkman, TanakaPotential: D D DTensor D D Dstructure:Tensorial structure of massive gravityVainshtein radius for DGP modelRelated to strong self interaction of the brane bending sectorC.D.,Gabadadze, Dvali, Vainshtein; Arkani-Hamed, Georgi Schwartz; Rubakov; Luty, Porrati, Rattazzi.
16 This has been generalized to cosmological backgrounds Lue, Starkman ’02(see also Dvali, Gruzinov,Zaldarriaga ‘02)GR termsCorrectiondepending on the cosmological phaseFor the EarthUniversal perihelion precessionBest prospect to detect this effect: lunar ranging experiments (BEPPI COLUMBO mission ?)
17 One can get effective (4D) equations of motion 2.3 Cosmological perturbations (linearized theory on a cosmological background)One can get effective (4D) equations of motionwhich have the form (e.g. for matter on the branewith vanishing anisotropic stress) C.D. ‘02Gravitationnal potentialsUsual 4D Einstein equationsBulk « Weyl fluid »anistropic stress…Has no local evolution equationThis has been put to zero by various authors for no good reasons (equivalent to « declare » that the model has no vDVZ discontinuity !)Correct analysis done by Lue, Scoccimarro, Starkman; Koyama, Maartens ) non standard growth of LSS,yields 8 < 0.8 (at two sigma level)
18 2. 4 The dark side of DGP gravity… andDvali, Gabadadze, Kolanovic, Nitti; Kiritsis, Tetradis, Tomaras; Antoniadis, Minasian, Vanhove; Kohlprath; Kohlprath, VanhoveNeed for a good underlying quantum gravity constructionMeaning of this strong coupling scale, UV completion at a scale even lower thanLuty, Porrati, Rattazzi; Dvali; Gabadadze; Nicolis, Rattazi; RubakovInteresting issues related to comparison between linearized solution and spherically symmetric perturbative solutionsGabadadze, Iglesias
19 A Ghost in the self accelerating phase Luty, Porrati, Rattazi; Nicolis, Rattazzi; Koyama; Gorbunov, KoyamaBut appears at the cutoff of the scalar part of the theory, also issues with the choice of boundary conditionsC.D. Gabadadze, Iglesias in preparationSibiryakov; Charmousis, Kaloper,Gregory, Padilla.Recent claim: no possible UV completion in awell-behaved theory ?Adams, Arkani-Hamed, Dubovsky, Nicolis, RattazziNot in DGP model, but at best in some limit where gravity has been decoupled !
20 Conclusions DGP gravity Modifies gravity at large distances Has a well defined action principleAccelerates universe expansion with no c.c. and the same # of parameters as CDMCan be distinguished from CDMExciting observables linked to the « Vainshtein mechanism »: gravity is (also) modified at distances smaller than cosmologicalInteresting playground to investigate « massive gravity » (a candidate for a consistent theory of « massive gravity »)More work needed to enlightened the dark side!IN PARTICULAR, ONE SHOULD KEEP IN MIND THE LOW CUTOFF OF THE SCALAR PART OF THE THEORY… AS A CONSEQUENCE, COMPARISONS WITH PRECISION DATA ARE TO BE CONSIDERED WITH SOME CAUTION !