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Gravity and Extra Dimensions. José Santiago Theory Group (Fermilab). APS April meeting, Session Y4 (Gravity and Cosmology) Jacksonville (FL) April 14-17, 2007. Outline. Introduction Breakthrough: Braneworld gravity Understanding the Acceleration of the Universe

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## Gravity and Extra Dimensions

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**Gravity and Extra Dimensions**José Santiago Theory Group (Fermilab) APS April meeting, Session Y4 (Gravity and Cosmology) Jacksonville (FL) April 14-17, 2007**Outline**• Introduction • Breakthrough: Braneworld gravity • Understanding the Acceleration of the Universe • Infinite Extra Dimensions: DGP • Higher Codimension Branes and SUSY: SLED • Conclusions J. Santiago, Gravity and Extra Dimensions**Introduction**• Once upon a time (1920s) Kaluza and Klein tried to unify gravity and electromagnetism in 5 dimensions • The idea did not work .... • Gravity couples universally to energy ... and was forgotten for many years 4d scalar 4D graviton (GR) 4D vector (QED) J. Santiago, Gravity and Extra Dimensions**Introduction**• New motivation for Extra Dimensions came from string theory (1980s) • 6 extra dimensions are predicted in consistent string models • They were considered to be tiny small • Higher dimensional fields decompose in massless modes plus modes with masses • ED effects irrelevant at low energies J. Santiago, Gravity and Extra Dimensions**Braneworld Gravity**• String theory motivated a breakthrough in gravity and extra dimensions (1990s) • Gravity (closed strings) propagate the extra dimensions • Gauge theories (open strings) are stuck at branes Extra Dimensions Gauge boson Graviton J. Santiago, Gravity and Extra Dimensions**SM**ED Bulk Gravity Braneworld Gravity • Braneworld gravity allows many new possibilities J. Santiago, Gravity and Extra Dimensions**SM**ED Bulk Gravity Braneworld Gravity • Braneworld gravity allows many new possibilities • ADD (1998): 2 or more ED with R~0.1 mm~1/(10-4 eV) are allowed • RS (1999): Infinite (strongly curved) ED are allowed • DGP (2000): Even infinite flat ED are allowed ... and could explain the acceleration of the Universe • ... J. Santiago, Gravity and Extra Dimensions**Understanding the Acceleration of the Universe**• The Universe is currently accelerating • All cosmological data agrees very well with a cosmological constant • It’s 60 orders of magnitude smaller than expected! J. Santiago, Gravity and Extra Dimensions**Extra-dimensional takes at the Cosmological Constant problem**J. Santiago, Gravity and Extra Dimensions**Dvali-Gabadadze-Porratti Model**• DGP: Gravitational action in M5 plus a flat brane with an induced Einstein-Hilbert term Generated by quantum corrections J. Santiago, Gravity and Extra Dimensions**Dvali-Gabadadze-Porratti Model**• DGP: Gravitational action in M5 plus a flat brane with an induced Einstein-Hilbert term • Gravity due to a bound state of the continuum of graviton KK modes • Modification of gravity at large (cosmological) scales • 4D at short distances but turn 5D at large distances Dvali, Gabadadze, Porratti ’00; ... Generated by quantum corrections J. Santiago, Gravity and Extra Dimensions**DGP Cosmology**• Modified Friedman equation with two branches Deffayet ’01; Deffayet, Dvali, Gabadadze ’02; ... • Standard branch (-) • Standard early cosmology • 5D late time cosmology • Selfaccelerating branch (+) • Standard early cosmology • Late time acceleration J. Santiago, Gravity and Extra Dimensions**Comparison with Experiment**Song, Sawicki, Hu ‘06 • Flat DGP excluded by geometrical probes • Open DGP only marginally worse than flat ΛCDM (1 extra parameter) • Non-geometrical probes can tell DGP and ΛCDM apart J. Santiago, Gravity and Extra Dimensions**Caveats**Vainshtein ’72; Deffayet, Dvali, Gabadadze, Vainshtein ’01; Gruzinov ’01; Luty, Porrati, Rattazzi ’03; Rubakov ’03 • There is an intrinsic strong coupling in the model • Difficult to compute solutions valid at all scales • Ghosts (negative energy states) present in linear perturbations around the selfaccelerating branch • The model may have problems with a local, causal, unitary UV completion • Might be solved at the non-linear level • Not obvious solution (yet) to the cosmological constant problem Luty, Porrati, Rattazzi ’03; Nicolis, Rattazzi ’04; Koyama ’05; Gorbunov, Koyama, Sibiryakov ’05; Charmousis, Gregory, Kaloper, Padilla ’06; Carena, Lykken, Park, Santiago ‘06 Adams, Arkani-Hamed, Dubovsky, Nicolis, Rattazzi ‘06 J. Santiago, Gravity and Extra Dimensions**Generalizations of DGP**Bao, Carena, Lykken, Park, Santiago ’05-06 • Let us consider a more general model with a negative bulk cosmological constant and two branes with arbitrary tensions and localized curvature terms • We can have (Anti) de Sitter or flat branes at an arbitrary separation • Bulk curvature can help understand problems J. Santiago, Gravity and Extra Dimensions**Generalizations of DGP**Bao, Carena, Lykken, Park, Santiago ’05-06 • We can study all the models at once, as a function of the input parameters • We have not found completely ghost-free solutions but there are examples of self-accelerating solutions with a ghost that is different from the one in DGP No DGP ghost There is a massless graviton ghost that does not decouple in the limit of an infinite extra dimension J. Santiago, Gravity and Extra Dimensions**Supersymmetric Large Extra DimensionS (SLEDS)**Aghababaie, Burgess, Parameswaran, Quevedo ’04 • Brane with two extra dimensions • Brane tension does not curve the bulk • Conical singularity that cancels the brane tension • Supersymmetry cancels out quantum corrections to the cosmological constant above MSUSY J. Santiago, Gravity and Extra Dimensions**SLEDS**• The Model: • 6D Supergravity with two 3-branes • Compactification by fluxes with R~0.1 mm • Conical singularities at brane locations flat branes J. Santiago, Gravity and Extra Dimensions**SLEDS**• The Model: • 6D Supergravity with two 3-branes • Compactification by fluxes with R~0.1 mm • Conical singularities at brane locations flat branes • Most general solution with axial symm. and maximally 4D symm. has flat branes Gibbons, Guvens, Pope, 03 J. Santiago, Gravity and Extra Dimensions**SLEDS**• Contribution to low-energy cosmological constant: • Brane tension: SUSY badly broken on the brane • Classical bulk contribution: conical singularity • Bulk quantum contribution: determined by bulk SUSY J. Santiago, Gravity and Extra Dimensions**Caveats**• Fundamental explanation of scales • How to explain 0.1 mm extra dimensions? • But relates hierarchy and cosmological constant problems • Detailed analysis of dynamics of relaxation • Higher curvature terms • Thick branes • Quantum corrections might be too big • Will be experimentally tested in the near future Bostock, Gregory, Navarro, Santiago 04 Navarro, Santiago 05 J. Santiago, Gravity and Extra Dimensions**Conclusions**• Extra dimensions give a new perspective to gravity • Braneworlds: New freedom to attack old problems • DGP model: • Can explain acceleration without a cosmological constant • Strongly coupled: difficult to compute at all scales • SLEDS • Can explain the smallness of the “cosmological constant” • Full time-dependent equations difficult to solve • Not yet a solution to the CC problem but ... J. Santiago, Gravity and Extra Dimensions**It’s difficult to make predictions ... ...**especially about the future Yogi Berra J. Santiago, Gravity and Extra Dimensions

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