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

DGP gravity
Theory and
Phenomenology
From quantum to Cosmos
Fundamental Physics
Research in Space
Cédric Deffayet
(APC & IAP, Paris)
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 ?
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
Dark matter or dark
energy ?
1. The DGP model (or brane-induced gravity).
Dvali, Gabadadze, Porrati, 2000
5D Minkowski
bulk space-time
5D
Einstein
tensor
A « brane world » model:
our 4D space-time is a
surface embedded in a
large space-time
Special equations of
motion for gravity
If equal to zero, standard, 4D,
Einstein equations (~ = c =1)
Brane localization
Action principle for this
Usual 5D brane
world action
Peculiar to
DGP model
A special hierarchy between
M(5) and MP is required
to render the model
phenomenologically interesting
• Brane localized kinetic
term for the graviton
• Will generically be induced
by quantum corrections
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
4D D’Alembertian
Source for 
For a localized static
source, one find the
following response
5D potential at
large distances
Transition
4D potential at
small distances
Back to the DGP model :
• Newtonian potential on the brane behaves as
V(r ) /
V(r ) /
1
r
1
4D behavior at small distances
5D behavior at large distances
r2
• 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 (KaluzaKlein) 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!
The vDVZ discontinuity as seen in Schwarzschild-type
solution of « massive gravity » (DGP model, see thereafter!)
2
ds2 = à e÷(ú) dt 2 + eõ(ú) dú2 + eö(ú) ú2dÒ2
÷(r ) = à
õ(r ) = +
rS
7 …
+
r (1+ 32ï +
1
2
:::
rS
21
+ ï…
à
(1
r
8 +
with ï =
:::
rS
m4r 5
Vainshtein ‘72
Wrong light bending!
This coefficient equals +1
Introduces
a new length
scale r
in Schwarschild
solution
in the problem
below which the perturbation theory diverges!
V
For the sun: bigger than solar system!
with
r v = (r Smà 4)1=5
So, what is going on at smaller distances?
Vainshtein’s answer (1972):
There exists an other perturbative expansion at smaller
distances, reading:
÷(r ) = à
rS
r
õ(r ) = +
rS
r
n
ð
1+ O r
n
ð
1+ O r
ño
5=2
=r v
5=2
à1
r v / m 4=5
ño
5=2
=r v
5=2
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 cosmology
Depending on the
sign of
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
no R termfrom
on standard cosmology
Latebulk
timewith
deviation
Self accelerating solution
the brane (i.e.: solution to 5D
(asympotes de Sitter space
Einstein-Hilbert Action)
even with zero matter energy
density)
DGP self accelerating phase
The brane (first) Friedmann equation
Can be rewritten as
with
Phase diagram
with  = +1
Acts as a cosmological
constant if  = +1
Same number of
parameter as CDM
Maartens, Majerotto
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…..
• 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
structure:
4D
5D
5D
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 ?)
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
Bulk « Weyl fluid »
anistropic stress…
Usual 4D Einstein equations
Has no local evolution
equation
This has been put to zero by various authors
Correct analysis
donereasons
by Lue,
Scoccimarro,
Starkman;
for no good
(equivalent
to « declare
»
that the model
no vDVZ growth
discontinuity
!)
Koyama, Maartens
) nonhas
standard
of LSS,
yields 8 < 0.8 (at two sigma level)
2. 4 The dark side of DGP gravity…
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
Luty, Porrati, Rattazzi; Dvali;
scale even lower than
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
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 !
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 !