DGP gravity Theory and Phenomenology 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

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 the success/failure of both approaches: Le Verrier and The discovery of Neptune The non discovery of Vulcan… but that of General Relativity

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 Standard model 5D Minkowski bulk space-time Special equations of motion for gravity 5D Einstein tensor Brane localization If equal to zero, standard, 4D, Einstein equations (~ = c =1)

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

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) Theoretical interest Consistent (?) non linear massive gravity …

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 Transition

Newtonian potential on the brane behaves as Back to the DGP model : Newtonian potential on the brane behaves as 4D behavior at small distances 5D behavior at large distances 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. 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!

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 ‘72 Wrong light bending! Introduces a new length scale r in the problem below which the perturbation theory diverges! V For the sun: bigger than solar system!

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

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 equation With C.D. ‘01 Analogous to standard (4D) Friedmann equations for small Hubble radii Early cosmology as usual

Late time deviation from standard cosmology Late time cosmology Depending on the sign of Self 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

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

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

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 for localized relativistic source showing the same recovery…..

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, Tanaka Potential: 4D 4D 5D Tensor 4D 5D 5D structure: Tensorial structure of massive gravity Vainshtein radius for DGP model Related to strong self interaction of the brane bending sector C.D.,Gabadadze, Dvali, Vainshtein; Arkani-Hamed, Georgi Schwartz; Rubakov; Luty, Porrati, Rattazzi.

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

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 motion which have the form (e.g. for matter on the brane with vanishing anisotropic stress) C.D. ‘02 Gravitationnal potentials Usual 4D Einstein equations Bulk « Weyl fluid » anistropic stress… Has no local evolution equation This 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)

2. 4 The dark side of DGP gravity… and Dvali, Gabadadze, Kolanovic, Nitti; Kiritsis, Tetradis, Tomaras; Antoniadis, Minasian, Vanhove; Kohlprath; Kohlprath, Vanhove Need for a good underlying quantum gravity construction 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

A Ghost in the self accelerating phase Luty, Porrati, Rattazi; Nicolis, Rattazzi; Koyama; Gorbunov, Koyama 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 Sibiryakov; Charmousis, Kaloper,Gregory, Padilla. 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 !

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 ») 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 !