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## THE UNIVERSE AS A BRANE

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**THE UNIVERSE AS A BRANE**Roy Maartens Portsmouth QG05 Sardegna**general relativity + particle physics:expanding 4D universe**model confirmed by observations**the model fits the high-precision data**SDSS WMAP**GR + SM particle physics:inflationary LCDM model**• successful model • but we know GR breaks down • quantum gravity will explain (pre-) inflation**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?**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**string theory**• removes the infinities of QFT • and includes the graviton • but there is a price … 9 space dimensions!! 6 compact 3**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**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)**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**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**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**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**cosmology probes gravity on vast scales**(Tegmark)**eg - SDSS test of Newton’s law**cccc (Shirata et al)**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?**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)**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 • ….**small extra dimensions**(moduli stabilised) exp(-y/L) visible brane shadow brane brane anti de Sitter 5D (infinite extra dimension) L large extra dimension**all extra dimensions large**(Antoniadis, Arkani-Hamed, Dimopoulos, Dvali 1998) brane n-torus identify (…. Antoniadis talk)**testing gravity in the laboratory**• extra dimension changes Newton’s law torsion pendulum L**(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**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**time**cosmic expansion = movement of brane 3D space**deviation from 4D GR in the early universe**• modified Friedmann equation • gravity leakage: gravity becomes 5D gravity leakage (Binetruy, Deffayet, Langlois) (Shiromizu, Maeda, Sasaki)**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)**modified background boosts 4D GW**• but 5D GW emission damps 4D GW • competing effects – cancel! recover GR result (Hiramatsu,Koyama,Taruya)**BH**time bulk brane CMB anisotropies • 5D BH induces “dark radiation” on the brane perturbation isocurvature perturbation • 5D anisotropy induces anisotropic stress BH**Spectralindex**simple model constraint on small BH mass in 5D bulk spacetime BH mass probability 00 (Koyama)**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**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?**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**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**DGP cosmology**Friedmann (Deffayet) • early universe – recover GR dynamics • late universe – acceleration without dark energy * from leakage of gravity * but fine-tuned**comparison with SNe observations**(Deffayet et al) (Sahni et al) (Song) (Bento talk)**structure formation**• degeneracy between DGP and GR+DE: both can fit SNe observations but this is broken by structure formation**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**CMB – the ISW effect**difference in LSS formation will leave an imprint (Nichol)**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)**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!**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