Brane-world gravity: progress and problems…

David Langlois APC & IAP, Paris Outline

• 4D point of view – Brane inflation (KKLT, etc…)

•5Dmodels – Randall-Sundrum 2 • cosmological perturbations • black holes –DGP – Two-brane models (RS1, collisions)

• Higher dimensions – Large extra dimensions (ADD): black holes – Codimension 2 branes 4D point of view

• Inflation from string theory – Brane inflation: inflaton as the distance between two branes effective 4D scalar

– Flux compactification (to stabilize the various moduli): KKLT • 4D supergravity with for the volume modulus T • AdS minimum with stabilized moduli • Lifted to dS by adding anti-D3-brane 4D point of view

Probe D3-brane in warped geometry

– KKLMMT – DBI inflation

Constraints from observations: - scalar spectrum, tensor spectrum - non-gaussianities Talk by J. Lidsey Other models: racetrack, … 5D point of view

• Qualitatively new effects : go around 4D results (e.g. transplanckian effects: talk V. Rubakov)

• Self-gravity of branes junction conditions (simple for codimension 1)

• Three main models: 1. Randall-Sundrum 2 (single brane) – Cosmology – Black holes 2. DGP 3. Randall-Sundrum 1 (two branes) Randall-Sundrum 2

• Static case

• Cosmology

Brane moving in the static geometry RS cosmology: cosmological perturbations

Brane inflation (scalar field localized on the brane) 1. Scalar perturbations Extension of the 4D formula (ignoring bulk perturbations)

– but brane perturbations strongly coupled to bulk perturbations – need to quantize the coupled brane-bulk system

Talks by Mennim, Mizuno (& Hiramatsu)

2. Tensor perturbations Evolution of tensor modes

• The 4D tensor modes satisfy the wave equation

• For k¿ aH, h4d is constant, whereas, inside the Hubble radius, h4d behaves like a-1.

• Taking into account only the change of homogeneous cosmology, 4/3 one finds Ωgw/k for modes entering the Hubble radius in the high energy (radiation) era. • Five-dimensional effects:

–k¿aH, h5d constant –k/a>H>µ, massive modes produced damping of the zero mode

• What is the relative strength of the two effects ?...

Hiramatsu ‘06 Evolution of tensor modes

Numerical analysis • Ichiki & Nakamura ’03 • Hiramatsu, Koyama & Taruya ‘04 • Kobayashi & Tanaka ‘05 • Seahra ’06 • Hiramatsu ‘06

• For a radiation-dominated universe, the two effects compensate identical to 4D results !

• Eq of state p=w ρ Beyond highly symmetric solutions

• Cosmology easy because highly symmetric • More complicated situations ? – Effective 4D Einstein equations

Projected Weyl tensor Eµν Effective energy-momentum tensor for a “Weyl” fluid

– In most cases, one needs to solve for the bulk geometry Search for explicit brane-bulk solutions 1. Solve analytically 2. Known bulk solution sliced by a brane brane matter content dictated by the bulk (ex: anisotropic cosmology) 3. Numerical solutions (ex: brane stars, black holes) Example: anisotropic brane cosmology

[Fabbri, DL, Steer, Zegers ’04] • Anisotropic (Bianchi I) cosmology in the brane:

• Starting from an anisotropic bulk metric ansatz,

one can find a solution of 5D vacuum Einstein’s eqs

with Anisotropic brane cosmology • In general, a brane embedded in an anisotropic bulk spacetime must contain matter with anisotropic stress, because of the junction conditions: – isotropic part:

– anisotropic part:

• For , one can embed a moving brane with perfect fluid type matter.

• Effective cosmological equation of state: Brane black holes

Question: RS version of the usual 4D Schwarzschild BH ? – Black string but singular unstable – No analytical solution found so far… – Conjecture (Tanaka; Emparan, Fabbri, Kaloper): a static solution should not exist.

AdS/CFT correspondence: classical 5D solution 4D BH + quantum corrections

no static 5D solution Hawking radiation

– Numerical approach (Kudoh) -> numerical solutions, apparently static, for relatively small BH Brane induced gravity DGP model (Dvali-Gabadadze-Porrati)

• Critical lengthscale

Gravity is 5-dim for r > rc

• Pertubative treatment breaks down below

[ Vainshtein ]

[Lue, Phys. Rep.] Brane induced gravity

• Cosmological solutions

Friedmann

• : self-accelerating solution • : “normal” solution

• Ghost problem ! Gorbunov, Koyama, Sibiryakov Charmousis, Gregory, Kaloper, Padilla – Linearized perturbations about Deffayet, Gabadadze, Iglesias self-accelerating solution ghost classically unstable – Maybe not the end of the story ? Models with two branes

• Randall-Sundrum 1

Effective 4D theory Talks T. Shiromizu & S. Fujii - in the low energy limit - In the close brane limit - 3-brane models Collision of branes

• Ekpyrotic/cyclic scenario … but also other models – New point of view on the Big-Bang – Alternative to inflation ? Problem of the spectrum of perturbations

• Explicit dynamical solutions – Collision of D3-branes Talk G. Gibbons – Collision of the two branes in HW model

Collision of two 5D domain walls (see talk K. Maeda) Higher dimensions (D>5)

• Large extra dimensions (Arkani-Hamed, Dimopoulos, Dvali)

• Self-gravitating branes - codimension 2 branes - codimension 1 branes which are compactified

Talk by J.Soda • String gas cosmology Production and decay of BHs

• Production of BH in particle scattering (TeV gravity relevant for the LHC)

1. 2.

• Higher-dim Schwarzschild-like or Kerr-like BHs

Spectrum of Hawking radiation depends on number of xtra dims (greybody factors) Talk P. Kanti • But the BH might escape from the brane…

Frolov & Stojkovic ‘02

Flachi & Tanaka ‘05 Self-gravitating codim 2 branes

Issues: 1. Stability of the compactification (flux) 2. Recovery of Einstein gravity on the brane 3. Self-tuning (cosmological constant problem) 4. Energy-momentum tensor on the string-like brane (only tension can be localized on a codimension 2 brane)

• SLED (Supersymmetric Large Extra Dimensions) Talk C. Burgess

Talks by Minamitsuji, Tasinato, Seto Conclusions…

• Discussion and rest of the workshop…

• Thanks to all the speakers !

• Thanks to the local organizers !