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  1. THE UNIVERSE AS A BRANE Roy Maartens Portsmouth QG05 Sardegna

  2. general relativity + particle physics:expanding 4D universe model confirmed by observations

  3. WMAP satellite and SDSS telescope

  4. the model fits the high-precision data SDSS WMAP

  5. 3 independent data sets intersect

  6. GR + SM particle physics:inflationary LCDM model • successful model • but we know GR breaks down • quantum gravity will explain (pre-) inflation

  7. inflation is not the only puzzle …. • dark energy?? maybe an IR modification to GR? (as well as UV in the early universe) • LCDM is a framework seeking a fundamental theory • more puzzles to come from observations?

  8. is high-precision cosmology probing the limits of GR? • inflation is crucial – what underlies it? • what is dark energy – matter or gravity? • GR must break down in the UV we need quantum gravity in the early universe +… maybe also in the late universe/ IR? • candidate theories (Kiefer 2004) quantum GR (Williams, Markopolou talks) string theory

  9. string theory • removes the infinities of QFT • and includes the graviton • but there is a price … 9 space dimensions!! 6 compact 3

  10. simple observation: we live in a large 3D world

  11. why don’t we see the extradimensions? • conventional Kaluza-Klein idea: extra dimensions too small to be seen • discovery of D-brane • matter fields restricted to lower dimensional brane • external bulk felt only through gravity • extra dimensions can be much larger 4Dspacetime small extra dimension ~ Lp large extra dimension >> Lp gravity matter

  12. (Tanaka)

  13. 1+9 D universe has branes and strings • some of the 6D may be small 5 string theories + supergravity = limits of 1+10 D theory M THEORY (Bousso, Nicolai, Stelle, Zanelli talks)

  14. string theory -the cosmologist’s wish-list*a natural mechanism for 3 dimensions to grow very large/ 6 dimensions to compactify* a natural mechanism for inflation* or … an alternative - eg brane collision * solve the dark energy problem…. then we test the answers COSMOLOGY AS A PROBE OF STRING THEORY

  15. but … string theory is tough! • no convincing stringy inflation yet • no convincing stringy dark energy yet • no convincing progress on perturbations • some progress in string brane inflation *D/ anti-D brane models * higher-Dcosmic strings can be produced * … but still a long way to go

  16. the practical cosmologist’s approach while waiting for progress in string cosmology … develop phenomenology * it’s what we do with inflation * and QG phenomenology(Liberati talk) use string theory ideas in cosmology * in fact this can help string theory … * brings high-precision data into the picture

  17. experimental tests of gravity • Cavendish • neutrons (Bertolami talk) • colliders (Cavaglia) • solar system perihelion bending of light • binary pulsars • gravitational lensing • BHs and GWs • cosmology • BBN, SNe • LSS, CMB

  18. cosmology probes gravity on vast scales (Tegmark)

  19. eg - SDSS test of Newton’s law cccc (Shirata et al)

  20. extra-dimensional gravity brings new features • extra polarizations of the graviton (KK modes) • new fields (dilaton, moduli, radion, form fields) • shadow matter • holography (AdS/CFT) (Bianchi talk) • precision data constrains extra-dimensional gravity • … hopefully rule out some models • signature of extra dimensions • in observations?

  21. graviton KK modes 5D gravitons – effective mass on brane (massive KK modes) polarizations:5 = 2+2+1 5D spin-2 (5) = 4D spin-2 (2) + 4D spin-1 (2) + 4D spin-0 (1)

  22. start with simple models • similar to inflation and dark energy models • simplest models with predictive power • focus on one or two key aspects at a time • KK modes of graviton • scalar fields – dilaton, radion, moduli • …. • motivate by string theory • 2 branes with large separation + small internal space (Horava-Witten) • AdS5 X M models: 1 large dimension, warped • ….

  23. small extra dimensions (moduli stabilised) exp(-y/L) visible brane shadow brane brane anti de Sitter 5D (infinite extra dimension) L large extra dimension

  24. all extra dimensions large (Antoniadis, Arkani-Hamed, Dimopoulos, Dvali 1998) brane n-torus identify (…. Antoniadis talk)

  25. testing gravity in the laboratory • extra dimension changes Newton’s law torsion pendulum L

  26. (Randall & Sundrum 1999) 5D solution of Einstein equations warped geometry • extra dimension shrinks toward infinity • finite volume bulk • curvature scale 4D GR is recovered on large scales y

  27. KK modes of the graviton (Garriga, Tanaka) Discrete spectrum • m=0: zero mode for tensors • no zero-mode for scalars/ vectors Continuous spectrum • m>0: massive KK modes of the graviton • same massive modes for scalar/ vector/ tensor U(z) d • ~ z –2 (de Risi talk) z

  28. time cosmic expansion = movement of brane 3D space

  29. deviation from 4D GR in the early universe • modified Friedmann equation • gravity leakage: gravity becomes 5D gravity leakage (Binetruy, Deffayet, Langlois) (Shiromizu, Maeda, Sasaki)

  30. RS inflation 5D metric perturbation • modified Friedmann • boosts 4D perturbations • but also creates 5D GW * back-reaction of 5D metric perturbations * loss of power • large scales boosted • but small scales? * Vinf lowered * AS and AT boosted * but AT/ AS suppressed (RM et al) (Langlois, RM, Wands) (Koyama,Mizuno,Wands)

  31. modified background boosts 4D GW • but 5D GW emission damps 4D GW • competing effects – cancel! recover GR result (Hiramatsu,Koyama,Taruya)

  32. BH time bulk brane CMB anisotropies • 5D BH induces “dark radiation” on the brane perturbation isocurvature perturbation • 5D anisotropy induces anisotropic stress BH

  33. Spectralindex simple model constraint on small BH mass in 5D bulk spacetime BH mass probability 00 (Koyama)

  34. is dark energy a gravitational effect? general relativity observations (nearly) flat, accelerating universe, with sub-critical matter field equations imply dark energy example from history Mercury perihelion – Newton + missing matter? no: modified gravity

  35. modify Einstein’s equations? try GR + light scalar field – same as DE field try ghosts try massive graviton (Pauli-Fierz) unstable theory try infinite extra degrees of freedom?

  36. braneworld models with late-time acceleration Randall-Sundrum modifies GR in UV (early universe) - via gravity leakage off the brane at early times recover GR in IR DGP model is an alternative (Dvali, Gabadadze, Porrati 2000) - gravity leakage off the brane at late times recover GR in UV L = crossover scale

  37. L = crossover scale: • 5D gravity dominates at late times • no graviton zero-mode: 4D gravity recovered at high energy via lightest KK modes ‘metastable graviton’ brane 5D Minkowski bulk: infinite volume extra dimension gravity leakage

  38. DGP cosmology Friedmann (Deffayet) • early universe – recover GR dynamics • late universe – acceleration without dark energy * from leakage of gravity * but fine-tuned

  39. need to test this against SNe redshifts

  40. comparison with SNe observations (Deffayet et al) (Sahni et al) (Song) (Bento talk)

  41. structure formation • degeneracy between DGP and GR+DE: both can fit SNe observations but this is broken by structure formation

  42. how to distinguish DGP from GR+DE? • structure formation is suppressed: * in GR – because DE dominates over matter * in DGP – because gravity weakens need to compute LSS and compare with SDSS L~1/H0

  43. CMB – the ISW effect difference in LSS formation will leave an imprint (Nichol)

  44. DE curve: scalar field model with the same background evolution as DGP DGP(4D) curve: neglects 5D term ISW effect gravity leakage must be taken into account …. SNe+SDSS+CMB may rule out DGP LCDM Dark Energy DGP (4D) (Takahashi)

  45. brane cosmology brings new ideas * new effects in inflation, CMB, dark energy - even in the simplest models * RS + DGP models – extra-D gravity is central (unlike string brane inflation models) * probe stringy ideas via gravity – and test against observations exciting challenges for theorists!

  46. string theory demands extra dimensions conclusion - the universe as a brane • this may explain the beginning of the universe • this may explain what inflation is • this may explain what the dark energy is • ….. but not yet - brane models can help