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 !.