ICHEP July 23 rd 2010 Modified Gravity and

What is Dark Energy ? Is it a Cosmological Constant ? ? ?

Degravitation Can Gravity be modified at Large Distances such that the CC gravitates more

Massive Gravity Filtering gravity is effectively a theory of massive gravity m 2 k

Worries 1. For pure vacuum energy, the metric remains flat But our Universe is

Relaxation mechanism The degravitation mechanism is a causal process. L Phase transition time H

Tuning / Fine-tuning From naturalness considerations, we expect a vacuum energy of the order

Tuning / Fine-tuning The amount of tuning is the same But the graviton mass

Worries 1. For a CC, the effective Newton Constant vanishes But our Universe is

Massive Gravity A massless spin-2 field in 4 d, has 2 dof A massive

Graviton mass To give the graviton a mass, include the interactions

Graviton mass To give the graviton a mass, include the interactions Mass for the

Fierz-Pauli mass To give the graviton a mass, include the interactions Ghost-like contribution: Disappear

Ghost-free decoupling limit Keeping this procedure to all orders in the decoupling limit pl

Properties Keeping this procedure to all orders, The Bianchi identity requires

Properties Keeping this procedure to all orders, The Bianchi identity requires Beyond 3 rd

The Galileon For a stable theory of massive gravity, the decoupling limit is The

EFT and relevant operators Higher derivative interactions are essential for the viability of this

Dirac Born Infeld One of the most attractive model of inflation is provided by

DBI - Galileon DBI is similar to the Galileon in that 1. It relies

Cosmological Puzzles Current Universe Massive gravity is one of the only model tackling the

Observational Signatures Such models lead to specific observational signatures Due to extra scalar field

Slides: 35

Download presentation

ICHEP July, 23 rd 2010 Modified Gravity and Degravitation Work with Gia Dvali, Gregory Gabadadze, Justin Khoury, Stefan Hofmann, Oriol Pujolas, Michele Redi, Andrew Tolley Claudia de Rham Université de Genève

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 ? ? ? � 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 ? ? ? � 120 orders of magnitude discrepancy! Is the cosmological constant small or does it have a small effect on the geometry

Degravitation Can Gravity be modified at Large Distances such that the CC gravitates more weakly? One naïve way to modify gravity is to promote the Newton’s constant GN to a high pass filter operator, L-2 Arkani-Hamed, Dimopoulos, Dvali &Gabadadze, ‘ 02 Dvali, Hofmann & Khoury, ‘ 07 k: 4 d momentum

Massive Gravity Filtering gravity is effectively a theory of massive gravity m 2 k 2

Worries 1. For pure vacuum energy, the metric remains flat But our Universe is accelerating !!!

Relaxation mechanism The degravitation mechanism is a causal process. L Phase transition time H 2 1/m time

Worries 1. For pure vacuum energy, the metric remains flat But our Universe is accelerating !!! The Universe keeps accelerating while relaxing towards the static solution 2. How does it help with the tuning issue?

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

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 0 The theory is tuned but technically natural ‘t Hooft naturalness argument

Worries 1. For a CC, the effective Newton Constant vanishes But our Universe is accelerating !!! The Universe keeps accelerating while relaxing towards the static solution 2. How does it help with the tuning issue? The theory is tuned but technically natural 3. How many degrees of freedom is there ?

Massive Gravity A massless spin-2 field in 4 d, has 2 dof A massive spin-2 field, has 5 dof

Graviton mass To give the graviton a mass, include the interactions

Graviton mass To give the graviton a mass, include the interactions Mass for the fluctuations around flat space-time Tensor Stückelberg field

Fierz-Pauli mass To give the graviton a mass, include the interactions 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 the decoupling limit pl with the scale fixed, we get

Ghost-free decoupling limit Keeping this procedure to all orders in the decoupling limit pl with the scale with fixed, we get

Properties Keeping this procedure to all orders, The Bianchi identity requires

Properties Keeping this procedure to all orders, The Bianchi identity requires Beyond 3 rd order, all the transverse tensors at ith order in p vanish identically.

Properties Keeping this procedure to all orders, The Bianchi identity requires Beyond 3 rd order, all the transverse tensors at ith order in p vanish identically. is at most 2 nd order in time derivative !

The Galileon For a stable theory of massive gravity, the decoupling limit is The interactions have 3 special features: 1. They are local 2. They possess a Shift and a Galileon symmetry 3. They have a well-defined Cauchy problem (eom remain 2 nd order) Correspond to the Galileon family of interactions Luty, Porrati, hep-th/0303116 Nicolis, Rattazzi and Trincherini, 0811. 2197 Cd. R, Gabadadze, 1007. 0443

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 theory Vainshtein, Phys. Lett. B 39 (1972) 393 Babichev, Deffayet & Ziour, 0901. 0393 Luty & Porrati, hep-th/0303116 Nicolis & Rattazzi, hep-th/0404159 Cd. R &Tolley, 1003. 5917

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 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 Luty & Porrati, hep-th/0303116 Nicolis & Rattazzi, hep-th/0404159 Cd. R &Tolley, 1003. 5917

Dirac Born Infeld One of the most attractive model of inflation is provided by the DBI action Which describes the dynamics of a probe-brane in a extra dimension Kabat and Lifschytz, hep-th/9902073

DBI - Galileon DBI is similar to the Galileon in that 1. It relies on higher derivative interactions, 2. While keeping quantum corrections under control 3. 4. It exhibits a 5 d Poincaré or Ad. S symmetry It has a well-defined Cauchy problem

Cosmological Puzzles Current Universe Massive gravity is one of the only model tackling the cosmological constant problem Early Universe 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 welldefined Cauchy problem

Observational Signatures Such models lead to specific observational signatures Due to extra scalar field dof Due to modified Friedman eq. - 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) Lue, Scoccimarro & Starkman, ’ 04 Lue, ’ 05 Afshordi, Geshnizjani & Khoury, ’ 08 Scoccimarro, ’ 09 Khoury & Wyman, ’ 09 Chan & Scoccimarro, ‘ 09 Bognat, Cd. R, Wyman, to appear Dutta & Cd. R, in progress