Holographic self-tuning of the cosmological constant
Received: May
Holographic self-tuning of the cosmological constant
Christos Charmousis 0 2 4 7 9
Elias Kiritsis 0 2 4 5 6 9
Francesco Nitti 0 2 4 5 9
0 Department of Physics, University of Crete 71003 Heraklion , Greece
1 Institute for Theoretical and Computational Physics
2 Sorbonne Paris Cite , B
3 CNRS/IN2P3, CEA/IRFU , Obs. de Paris
4 Universite Paris-Saclay , 91405 Orsay , France
5 APC, Universite Paris 7
6 Crete Center for Theoretical Physics
7 Laboratoire de Physique Theorique , CNRS, Univ. Paris-Sud
8 atiment Condorcet , F-75205, Paris Cedex 13 , France
9 We compute the
We propose a brane-world setup based on gauge/gravity duality in which the four-dimensional cosmological constant is set to zero by a dynamical self-adjustment mechanism. The bulk contains Einstein gravity and a scalar eld. We study holographic RG ow solutions, with the standard model brane separating an in nite volume UV region and an IR region of nite volume. For generic values of the brane vacuum energy, regular solutions exist such that the four-dimensional brane is determined dynamically by the junction conditions. Analysis of linear uctuations shows that a regime of 4-dimensional gravity is possible at large distances, due to the presence of an induced gravity term. The graviton acquires an e ective mass, and a ve-dimensional regime may exist at large and/or small scales. We show that, for a broad choice of poat-brane solutions are manifestly stable and free of ghosts.
tentials
1 Introduction and summary 2
The self-tuning theory
Emergent gravity and the brane-world
Results and outlook
Field equations and matching conditions
The Poincare-invariant ansatz
Holographic interlude 2.3.1 2.3.2 UV region
IR region
The self-adjustment mechanism
Consistent self-tuning solutions
Concrete examples
2.6.1
2.6.2
Case study I: an IR-regular model
Case study II: a class of stable self-tuning models
3
Linear perturbations around at solutions
Bulk perturbations
Brane perturbations and rst junction condition
Gauge xing and second junction condition
1.1
1.2
2.1
2.2
2.3
2.4
2.5
2.6
3.1
3.2
3.3
4.1
4.2
5.1
5.2
5.3
5.4
5.5
1
B The holographic parameters and the integration constants
C Avoiding Weinberg's no-go theorem
{ i {
D Linearized bulk equations and matching conditions
D.1 Perturbed bulk equations
D.2 Brane perturbations and linearized junction conditions
D.3 Tensor junction conditions
D.4 Scalar junction conditions D.5 Gauge-invariant action for scalar modes
E
The bulk propagator for tensor modes
E.1 Large-p behavior E.2 Perturbation expansion for small-p E.3 Regularity of the small-p expansion
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70
eld theories for low-energy interactions are a general framework
addressing observable physics from particle physics to cosmology. While typically successful,
they have so far failed to address the cosmological constant problem, [1] (see also [2, 3]
and [4] for an updated review and references within). Indeed our main dynamical
theory underlying cosmology, General Relativity (GR), and those of particle physics, namely
quantum
eld theories in at space-time, seem to be incompatible when it comes to
vacuum energy.
Experiments (such as the Lamb shift [5] or the Casimir e ect [6]) indicate that any
particle will give zero-point energy contributions to the vacuum energy, [7]. These
contributions scale with the fourth power of the cut-o , which can be as high as the Planck
scale, the generically assumed UV cut-o
of any QFT. On the other hand, vacuum
energy couples to gravity as an e ective cosmological constant, which by Einstein's equations
gives rise to a non-zero space-time curvature. If we assume the existence of
supersymmetry broken at some scale
SUSY , then the cosmological constant is expected to be of
order O( 4SUSY ). Experiment states that such a scale must be quite larger than a TeV and
therefore supersymmetry cannot solve the cosmological constant conundrum.
For illustration purposes, we may simply consider the contributions to zero point energy
due to the electron: this provides a contribution to the vacuum energy of order O(me4).
According to the principle of equivalence for GR any form of energy gravitates. Due to
covariance, the vacuum energy gravitates as a cosmological constant.
Gravitationally, a positive cosmological constant will seed a de Sitter space-time with
a nite distance (curvature) scale, the de Sitter horizon scale1 (in the static frame). This
scale is inversely proportional to the square root of the cosmological constant. Putting
in the numbers for the vacuum energy due to the electron, would tell us that the size of
our Universe is comparable to the earth-moon distance, as Pauli was amused to note back
1A negative cosmological constant instead would give nite life-time for the universe.
{ 1 {
in 1920 (see references within [2]). Needless to say that the Universe will become a lot
smaller if we allow for heavier particles and higher UV scales or phase transitions in the
Universe (wh (...truncated)