Cé dric Deffayet (APC & IAP, Paris)

1. Cédric Deffayet (APC & IAP, Paris) DGP gravity Theory and Phenomenology From quantum to Cosmos Fundamental Physics Research in Space Q2C Warrenton 2006 1/ DGP model (in 5D) or « brane induced gravity » 2/ Cosmology and phenomenology

2. Changing the dynamics of gravity ? Why being interested in this model ? One way to modify gravity at « large distances » … and get rid of dark energy ? Dark matter or dark energy ? Historical example the success/failure of both approaches: Le Verrier and • The discovery of Neptune • The non discovery of Vulcan… • but that of General Relativity

3. Special equations of motion for gravity 5D Minkowski bulk space-time Standard model 5D Einstein tensor If equal to zero, standard, 4D, Einstein equations (~ = c =1) Brane localization 1. The DGP model (or brane-induced gravity). Dvali, Gabadadze, Porrati, 2000 A « brane world » model: our 4D space-time is a surface embedded in a large space-time

4. Standard model Usual 5D brane world action Peculiar to DGP model • Brane localized kinetic • term for the graviton • Will generically be induced • by quantum corrections Action principle for this A special hierarchy between M(5) and MP is required to render the model phenomenologically interesting

5. Theoretical interest Consistent (?) non linear massive gravity … DGP model Phenomenological interest A 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)

6. Transition How does that work ? A scalar toy model for DGP 5D D’Alembertian Source for  4D D’Alembertian For a localized static source, one find the following response 5D potential at large distances 4D potential at small distances

7. The crossover distance between the two regimes is given by This 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. Leads to the van Dam-Veltman-Zakharov discontinuity on Minkowski background! Back to the DGP model : • Newtonian potential on the brane behaves as 4D behavior at small distances 5D behavior at large distances • But the tensorial structure of the graviton propagator is that of a massive graviton (gravity is mediated by a continuum of massive modes)

8. The vDVZ discontinuity as seen in Schwarzschild-type solution of « massive gravity » (DGP model, see thereafter!) Wrong light bending! This coefficient equals +1 in Schwarschild solution Introduces a new length scale r in the problem below which the perturbation theory diverges! V For the sun: bigger than solar system! + … + … Vainshtein ‘72

9. So, what is going on at smaller distances? Vainshtein’s answer (1972): There exists an other perturbative expansion at smaller distances, reading: with This goes smoothly toward Schwarschild as m goes to zero No warranty that this solution can be matched with the other for large r! Boulware, Deser ‘72

10. a(t0) a(t) With Analogous to standard (4D) Friedmann equations for small Hubble radii Early cosmology as usual 2. Phenomenology of DGPmodel 2.1 homogeneous cosmology The dynamics of the scale factor a(t) of our 4D Universe (the brane) is governed by the modified Friedmann equation C.D. ‘01

11. 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 Self accelerating solution(asympotes de Sitter space even with zero matter energy density) Late time cosmology Depending on the sign of

12. Acts as a cosmological constant if  = +1 Phase diagram with  = +1 Maartens, Majerotto DGP self accelerating phase The brane (first) Friedmann equation Can be rewritten as with Same number of parameter as CDM

13. Strictly speaking, only SN observations are depending solely on the background evolutions CMB and more importantly Baryon oscillations should be re-computed taking into account the peculiarities of DGP gravity Vs. CDM Maartens, Majerotto ‘06 DGP

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 rc small rc Solution of 4D GR with cosmic fluid Solution of 5D GR with a brane source Comes 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 forlocalized relativistic source showing the same recovery…..

15. Related to strong self interaction of the brane bending sector C.D.,Gabadadze, Dvali, Vainshtein; Arkani-Hamed, Georgi Schwartz; Rubakov; Luty, Porrati, Rattazzi. • Perturbative study of Schwarzschild type solutions of DGP model on a flat background space-time: Gruzinov, Porrati, Lue, Lue & Starkman, Tanaka Potential: 4D 4D 5D Tensor 4D 5D 5D structure: Tensorial structure of massive gravity Vainshtein radius for DGP model

16. For the Earth This has been generalized to cosmological backgrounds Lue, Starkman ’02 (see also Dvali, Gruzinov, Zaldarriaga ‘02) GR terms Correction depending on the cosmological phase Universal perihelion precession Best prospect to detect this effect: lunar ranging experiments (BEPPI COLUMBO mission ?)

17. Gravitationnal potentials Bulk « Weyl fluid » anistropic stress… Has no local evolution equation Usual 4D Einstein equations This has been put to zero by various authors for no good reasons (equivalent to « declare » that the model has no vDVZ discontinuity !) 2.3 Cosmological perturbations (linearized theory on a cosmological background) One can get effective (4D) equations of motion which have the form (e.g. for matter on the brane with vanishing anisotropic stress) C.D. ‘02 Correct analysis done by Lue, Scoccimarro, Starkman; Koyama, Maartens) non standard growth of LSS, yields 8< 0.8 (at two sigma level)

18. and Need for a good underlying quantum gravity construction Dvali, Gabadadze, Kolanovic, Nitti; Kiritsis, Tetradis, Tomaras; Antoniadis, Minasian, Vanhove; Kohlprath; Kohlprath, Vanhove Meaning of this strong coupling scale, UV completion at a scale even lower than Luty, Porrati, Rattazzi;Dvali; Gabadadze; Nicolis, Rattazi; Rubakov Interesting issues related to comparison between linearized solution and spherically symmetric perturbative solutions Gabadadze, Iglesias 2. 4 The dark side of DGP gravity…

19. Luty, Porrati, Rattazi; Nicolis, Rattazzi; Koyama; Gorbunov, Koyama Sibiryakov; Charmousis, Kaloper,Gregory, Padilla. But appears at the cutoff of the scalar part of the theory, also issues with the choice of boundary conditions C.D. Gabadadze, Iglesias in preparation Recent claim: no possible UV completion in a well-behaved theory ? Adams, Arkani-Hamed, Dubovsky, Nicolis, Rattazzi Not in DGP model, but at best in some limit where gravity has been decoupled ! A Ghost in the self accelerating phase

20. 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 ! Conclusions DGP gravity • Modifies gravity at large distances • Has a well defined action principle • Accelerates universe expansion with no c.c. and the same # of parameters as CDM • Can be distinguished from CDM • Exciting observables linked to the « Vainshtein mechanism »: gravity is (also) modified at distances smaller than cosmological • Interesting playground to investigate « massive gravity » (a candidate for a consistent theory of « massive gravity »)