Modified Gravity and Degravitation
-
Upload
augustine-lloyd -
Category
Documents
-
view
213 -
download
0
description
Transcript of Modified Gravity and Degravitation
Modified Gravity and Degravitation
ICHEP July, 23rd 2010 Modified Gravity and Degravitation Thank for
the invitation, its a pleasure to be here. Today I talk about the 2
hierarchy problems that exist at the interface between particle
physics and cosmology, more precisely when putting together the 3
standard forces with gravity and show how extra dimensions, and in
particular 2 or more large extra dimensions provide very fruitful
new directions to tackle them Work with Gia Dvali, Gregory
Gabadadze,Justin Khoury, Stefan Hofmann,Oriol Pujolas, Michele
Redi, Andrew Tolley Claudia de Rham Universit de Genve What is Dark
Energy ? Is it a Cosmological Constant ??? What is Dark Energy ? Is
it a Cosmological Constant ???
120 orders of magnitude discrepancy! What is Dark Energy ? Is it a
Cosmological Constant ??? OR
120 orders of magnitude discrepancy! OR Is Dark Energy is Dynamical
?? new form of energy eg. Quintessence, or self-accelerating
Universe eg. F(R), DGP What is Dark Energy ? Is it a Cosmological
Constant ??? OR
120 orders of magnitude discrepancy! OR Is Dark Energy is Dynamical
?? new form of energy eg. Quintessence, or self-accelerating
Universe eg. F(R), DGP These degrees of freedom must be extremely
light! What is Dark Energy ? Is it a Cosmological Constant
???
120 orders of magnitude discrepancy! Is the cosmological constant
smallordoes it have a small effect on the geometry Degravitation
Can Gravity be modified at Large Distances such that the CC
gravitates more weakly? One nave way to modify gravity is to
promote the Newtons constant GN to a high pass filter operator, k:
4d momentum L-2 Arkani-Hamed, Dimopoulos, Dvali &Gabadadze, 02
Dvali, Hofmann & Khoury, 07 Massive Gravity Filtering gravity
is effectively a theory of massive gravity To see that, we can
simply look at the linearized Einstein equation. If I omit the
tensor structure for a second, the Einstein equation looks like k2
m2 Massive Gravity Filtering gravity is effectively a theory of
massive gravity To see that, we can simply look at the linearized
Einstein equation. If I omit the tensor structure for a second, the
Einstein equation looks like k2 m2 Worries But our Universe is
accelerating !!!
For pure vacuum energy, the metric remains flat But our Universe is
accelerating !!! To see that, we can simply look at the linearized
Einstein equation. If I omit the tensor structure for a second, the
Einstein equation looks like Relaxation mechanism L H2 time
The degravitation mechanism is a causal process. 1/m H2 time Phase
transition L To see that, we can simply look at the linearized
Einstein equation. If I omit the tensor structure for a second, the
Einstein equation looks like Relaxation mechanism L H2 time
The degravitation mechanism is a causal process. 1/m H2 time Phase
transition L To see that, we can simply look at the linearized
Einstein equation. If I omit the tensor structure for a second, the
Einstein equation looks like Worries But our Universe is
accelerating !!!
For pure vacuum energy, the metric remains flat How does it help
with the tuning issue? But our Universe is accelerating !!! The
Universe keeps accelerating whilerelaxing towards the static
solution To see that, we can simply look at the linearized Einstein
equation. If I omit the tensor structure for a second, the Einstein
equation looks like Tuning / Fine-tuning From naturalness
considerations, we expect a vacuum energy of the order of the
cutoff scale (Planck scale). But observations tell us For the
degravitation mechanism to work, the mass of the graviton should be
To see that, we can simply look at the linearized Einstein
equation. If I omit the tensor structure for a second, the Einstein
equation looks like but technically natural
Tuning / Fine-tuning The amount of tuning is the same But the
graviton mass remains stable against quantum corrections we recover
a symmetry in the limit m To see that, we can simply look at the
linearized Einstein equation. If I omit the tensor structure for a
second, the Einstein equation looks like The theory is tuned but
technically natural t Hooft naturalness argument but technically
natural
Worries For a CC, the effective Newton Constant vanishes How does
it help with the tuning issue? How many degrees of freedom is there
? But our Universe is accelerating !!! The Universe keeps
accelerating whilerelaxing towards the static solution Another
worry, which is I think more serious is to do with the tuning issue
which was the reason why we introduced this model in the first
place. The theory is tuned but technically natural Massive Gravity
A massless spin-2 field in 4d, has 2 dof
A massivespin-2 field, has 5 dof To see that, we can simply look at
the linearized Einstein equation. If I omit the tensor structure
for a second, the Einstein equation looks like Graviton mass To
give the graviton a mass, include the interactions
To see that, we can simply look at the linearized Einstein
equation. If I omit the tensor structure for a second, the Einstein
equation looks like Graviton mass To give the graviton a mass,
include the interactions
Mass for the fluctuations around flat space-time To see that, we
can simply look at the linearized Einstein equation. If I omit the
tensor structure for a second, the Einstein equation looks like
Tensor Stckelberg field Fierz-Pauli mass To give the graviton a
mass, include the interactions
To see that, we can simply look at the linearized Einstein
equation. If I omit the tensor structure for a second, the Einstein
equation looks like Ghost-like contribution: Disappear for the
Fierz-Pauli choice: This choice can be made to all orders !
Ghost-free decoupling limit
Keeping this procedure to all orders in thedecoupling limit with
the scale fixed, we get pl To see that, we can simply look at the
linearized Einstein equation. If I omit the tensor structure for a
second, the Einstein equation looks like Ghost-free decoupling
limit
Keeping this procedure to all orders in thedecoupling limit with
the scale fixed, we get with pl To see that, we can simply look at
the linearized Einstein equation. If I omit the tensor structure
for a second, the Einstein equation looks like Properties Keeping
this procedure to all orders,
The Bianchi identity requires To see that, we can simply look at
the linearized Einstein equation. If I omit the tensor structure
for a second, the Einstein equation looks like Properties Keeping
this procedure to all orders,
The Bianchi identity requires Beyond 3rd order, all the transverse
tensors at ithorder in p vanish identically. To see that, we can
simply look at the linearized Einstein equation. If I omit the
tensor structure for a second, the Einstein equation looks like
Properties Keeping this procedure to all orders,
The Bianchi identity requires Beyond 3rd order, all the transverse
tensors at ithorder in p vanish identically. is at most 2nd order
in time derivative ! To see that, we can simply look at the
linearized Einstein equation. If I omit the tensor structure for a
second, the Einstein equation looks like Properties Keeping this
procedure to all orders,
The Bianchi identity requires Beyond 3rd order, all the transverse
tensors at ithorder in p vanish identically. is at most 2nd order
in time derivative ! The linear and quadratic mixings can be
removed by a local field redefinition To see that, we can simply
look at the linearized Einstein equation. If I omit the tensor
structure for a second, the Einstein equation looks like The
Galileon For a stable theory of massive gravity, the decoupling
limit is The interactions have3 special features: They are local
They possessa Shift and a Galileon symmetry They have a
well-defined Cauchy problem (eom remain 2nd order) Before looking
at how these interactions affect observations, let me emphasize 3
very important characteristics of this model. First of all the
interactions are local, are derive from an action. Second they have
a specific symmetry which is a shift symmetry inheritated from 5d
diff invariance, And finally all the terms in the eom are at most
(and actually exactly) 2nd order in derivative, which means that
the system will have a well-defined cauchy problem and no ghost
like instabilities. Correspond to the Galileon family of
interactions Luty, Porrati, hep-th/ CdR, Gabadadze, Nicolis,
Rattazzi and Trincherini, EFT and relevant operators
Higher derivative interactions are essential for the viability of
this class of models. Within the solar system, p reaches the scale
L*,yet, we are still within the regime of validity of the theory
What is interesting to notice in this model is that we are working
in a regime where the interactions are important, but quantum
corrections are still well under control, and so the theory is not
breaking down. In particular the field can have a large velocity
but the amplitude of the quantum corrections small and still remain
under control. This is very important to be able to trust the
theory at the scale \Lambda_\star. And actually this is very
similar to what happens in another model which is to due this time
with the very early Universe. Luty & Porrati, hep-th/ Nicolis
& Rattazzi, hep-th/ Vainshtein, Phys. Lett. B 39 (1972) 393
Babichev, Deffayet & Ziour, CdR &Tolley, EFT and relevant
operators
Higher derivative interactions are essential for the viability of
this class of models. Within the solar system, p reaches the scale
L*,yet, we are still within the regime of validity of the theory
What is interesting to notice in this model is that we are working
in a regime where the interactions are important, but quantum
corrections are still well under control, and so the theory is not
breaking down. In particular the field can have a large velocity
but the amplitude of the quantum corrections small and still remain
under control. This is very important to be able to trust the
theory at the scale \Lambda_\star. And actually this is very
similar to what happens in another model which is to due this time
with the very early Universe. Luty & Porrati, hep-th/ Nicolis
& Rattazzi, hep-th/ Vainshtein, Phys. Lett. B 39 (1972) 393
Babichev, Deffayet & Ziour, CdR &Tolley, EFT and relevant
operators
Higher derivative interactions are essential for the viability of
this class of models. Within the solar system, p reaches the scale
L*,yet, we are still within the regime of validity of the theory
The breakdown of the EFT is not measured by but by itself gradients
should be small So we can trust a regime where as long as What is
interesting to notice in this model is that we are working in a
regime where the interactions are important, but quantum
corrections are still well under control, and so the theory is not
breaking down. In particular the field can have a large velocity
but the amplitude of the quantum corrections small and still remain
under control. This is very important to be able to trust the
theory at the scale \Lambda_\star. And actually this is very
similar to what happens in another model which is to due this time
with the very early Universe. Luty & Porrati, hep-th/ Nicolis
& Rattazzi, hep-th/ CdR &Tolley, Dirac Born Infeld One of
the most attractive model of inflation is provided by theDBI action
Which describes the dynamics of a probe-brane in a extra dimension
In particular, one of the most attractive models of inflation comes
from the DBI action, which describes the dynamics of a probe brane
in an extra dimension. Where the parameter pi is associated to the
brane position along the extra dimension, and we see that if the
brane is moving relativistically, we should introduce the Lorentz
factor here. Kabat and Lifschytz, hep-th/ DBI - Galileon DBI is
similar to the Galileon in that
It relies on higher derivative interactions, While keeping quantum
corrections under control It exhibits a 5d Poincar or AdS symmetry
It has a well-defined Cauchy problem This DBI model which is a
priori completely disconnected from the Galileon, shares a lot of
commun features with the Galileon. The first one is that higher
derivative interactions are important, but quantum corrections are
still kept under control. It also has a surprising underlying
symmetry which it inheritated from the 5d underlying theory. And
most importantly, the equations of motion remain 2nd order in
derivative, so the system has a well-defined Cauchy problem, and
does not have any ghost like instability. Cosmological Puzzles
Current Universe Early Universe
Massive gravity is one of the only model tackling the cosmological
constant problem The DBI brane model provides an attractive
realization of inflation Both models rely on specific higher
derivative interactions that remain under control at the quantum
level They have non-linearly realized symmetries and well-defined
Cauchy problem Both these models rely on the existence of higher
derivative interactions which remain under control at the quantum
level, And have a non-lilearly realized symmetry, inheritated from
the extra dimension. They can be seen as 2 limits of the same
underlying theory
Cosmological Puzzles Current Universe Early Universe Massive
gravity is one of the only model tackling the cosmological constant
problem The DBI brane model provides an attractive realization of
inflation And what I have shown is that both these models are
actually simply 2 different limits of the same underlying theory.
They can be seen as 2 limits of the sameunderlying theory
Observational Signatures
Such models lead to specific observational signatures Advance of
the perihelion (LLR) Structure formation Lyman-a forest (excess of
power)- CMB (excess power at short scales) - large bulk flows in
velocity surveys kinetic Sunyaev-Zeldovich ISW cross-correlation
(larger effect) Due to extrascalar field dof Due to modified
Friedman eq. This model is also very rich in observational
signatures. One of first difference from standard GR is that there
extra scalar dof. they are strongly coupled close to a massive
source so they lead to very weak signatures within the solar
system, but the advance of the perihelion of the moon for instance
around the earth is measured with such an accuracy that they are
just on the edge of being observable at LLR experiments. these
extra scalar modes will also lead to some effects in structure
formation. Another source of signature comes from the fact that the
Friedman eq. is modified and therefore can lead to different
observational signatures which are also just on the edge of being
observable, some of which have even been observed within 2 sigma.
Lue, Scoccimarro & Starkman, 04 Khoury & Wyman, 09 Lue
& Starkman, 04 Chan & Scoccimarro, 09 Lue, 05 Bognat, CdR,
Wyman, to appear Afshordi, Geshnizjani & Khoury, 08 Dutta &
CdR, in progress Scoccimarro, 09