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Gravity and Extra DimensionsJos? Santiago Theory Group (Fermilab) APS April meeting, Session Y4 (Gravity and Cosmology) Jacksonville (FL) April 14-17, 2007 |
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OutlineIntroduction Breakthrough: Braneworld gravity Understanding the Acceleration of the Universe Infinite Extra Dimensions: DGP Higher Codimension Branes and SUSY: SLED Conclusions APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions |
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IntroductionOnce 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) APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions |
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IntroductionNew 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 APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions |
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Braneworld GravityString 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 APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions |
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Braneworld GravityBraneworld gravity allows many new possibilities APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions |
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Braneworld GravityBraneworld 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 ... APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions |
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Understanding the Acceleration of the UniverseThe Universe is currently accelerating All cosmological data agrees very well with a cosmological constant It’s 60 orders of magnitude smaller than expected! APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions |
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Extra-dimensional takes at the Cosmological Constant problemAPS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions |
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Dvali-Gabadadze-Porratti ModelDGP: Gravitational action in M5 plus a flat brane with an induced Einstein-Hilbert term Generated by quantum corrections APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions |
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Dvali-Gabadadze-Porratti ModelDGP: 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 Generated by quantum corrections APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions Dvali, Gabadadze, Porratti ’00; ... |
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DGP CosmologyModified Friedman equation with two branches Standard branch (-) Standard early cosmology 5D late time cosmology Selfaccelerating branch (+) Standard early cosmology Late time acceleration APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions Deffayet ’01; Deffayet, Dvali, Gabadadze ’02; ... |
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Comparison with ExperimentFlat DGP excluded by geometrical probes Open DGP only marginally worse than flat ?CDM (1 extra parameter) Non-geometrical probes can tell DGP and ?CDM apart APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions Song, Sawicki, Hu ‘06 |
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CaveatsThere 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 APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions Vainshtein ’72; Deffayet, Dvali, Gabadadze, Vainshtein ’01; Gruzinov ’01; Luty, Porrati, Rattazzi ’03; Rubakov ’03 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 |
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Generalizations of DGPLet 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 APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions Bao, Carena, Lykken, Park, Santiago ’05-06 |
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Generalizations of DGPWe 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 APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions Bao, Carena, Lykken, Park, Santiago ’05-06 |
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Supersymmetric Large Extra DimensionS (SLEDS)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 APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions Aghababaie, Burgess, Parameswaran, Quevedo ’04 |
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SLEDSThe Model: 6D Supergravity with two 3-branes Compactification by fluxes with R~0.1 mm Conical singularities at brane locations flat branes APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions |
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SLEDSThe 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 APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions Gibbons, Guvens, Pope, 03 |
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SLEDSContribution 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 APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions |
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CaveatsFundamental 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 APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions Bostock, Gregory, Navarro, Santiago 04 Navarro, Santiago 05 |
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ConclusionsExtra 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 ... APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions |
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It’s difficult to make predictions .. ... especially about the future Yogi Berra APS meeting, April 17, 2007 J. Santiago, Gravity and Extra Dimensions |
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