1. Gravity and Extra Dimensions José Santiago Theory Group (Fermilab) APS April meeting, Session Y4 (Gravity and Cosmology) Jacksonville (FL) April 14-17, 2007

2. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 Outline Introduction Introduction Breakthrough: Braneworld gravity Breakthrough: Braneworld gravity Understanding the Acceleration of the Universe Understanding the Acceleration of the Universe Infinite Extra Dimensions: DGP Infinite Extra Dimensions: DGP Higher Codimension Branes and SUSY: SLED Higher Codimension Branes and SUSY: SLED Conclusions Conclusions

3. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 Introduction Once upon a time (1920s) Kaluza and Klein tried to unify gravity and electromagnetism in 5 dimensions Once upon a time (1920s) Kaluza and Klein tried to unify gravity and electromagnetism in 5 dimensions The idea did not work.... The idea did not work.... Gravity couples universally to energy Gravity couples universally to energy... and was forgotten for many years... and was forgotten for many years 4D graviton (GR) 4d scalar 4D vector (QED)

4. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 Introduction New motivation for Extra Dimensions came from string theory (1980s) New motivation for Extra Dimensions came from string theory (1980s) 6 extra dimensions are predicted in consistent string models 6 extra dimensions are predicted in consistent string models They were considered to be tiny small They were considered to be tiny small Higher dimensional fields decompose in massless modes plus modes with masses Higher dimensional fields decompose in massless modes plus modes with masses ED effects irrelevant at low energies ED effects irrelevant at low energies

5. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 Braneworld Gravity String theory motivated a breakthrough in gravity and extra dimensions (1990s) String theory motivated a breakthrough in gravity and extra dimensions (1990s) Gravity (closed strings) propagate the extra dimensions Gravity (closed strings) propagate the extra dimensions Gauge theories (open strings) are stuck at branes Gauge theories (open strings) are stuck at branes Extra Dimensions Graviton Gauge boson

6. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 Braneworld Gravity Braneworld gravity allows many new possibilities Braneworld gravity allows many new possibilities Gravity SM ED Bulk

7. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 Braneworld Gravity Braneworld gravity allows many new possibilities Braneworld gravity allows many new possibilities Gravity SM ED Bulk ADD (1998): 2 or more ED with R~0.1 mm~1/(10 -4 eV) are allowed 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 RS (1999): Infinite (strongly curved) ED are allowed DGP (2000): Even infinite flat ED are allowed... and could explain the acceleration of the Universe DGP (2000): Even infinite flat ED are allowed... and could explain the acceleration of the Universe......

8. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 Understanding the Acceleration of the Universe The Universe is currently accelerating The Universe is currently accelerating All cosmological data agrees very well with a cosmological constant All cosmological data agrees very well with a cosmological constant It’s 60 orders of magnitude smaller than expected! It’s 60 orders of magnitude smaller than expected!

9. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 Extra-dimensional takes at the Cosmological Constant problem

10. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 Dvali-Gabadadze-Porratti Model DGP: Gravitational action in M 5 plus a flat brane with an induced Einstein-Hilbert term DGP: Gravitational action in M 5 plus a flat brane with an induced Einstein-Hilbert term Generated by quantum corrections

11. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 Dvali-Gabadadze-Porratti Model DGP: Gravitational action in M 5 plus a flat brane with an induced Einstein-Hilbert term DGP: Gravitational action in M 5 plus a flat brane with an induced Einstein-Hilbert term Gravity due to a bound state of the continuum of graviton KK modes Gravity due to a bound state of the continuum of graviton KK modes Modification of gravity at large (cosmological) scales Modification of gravity at large (cosmological) scales 4D at short distances but turn 5D at large distances 4D at short distances but turn 5D at large distances Generated by quantum corrections Dvali, Gabadadze, Porratti ’00;...

12. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 DGP Cosmology Modified Friedman equation with two branches Modified Friedman equation with two branches Deffayet ’01; Deffayet, Dvali, Gabadadze ’02;... Standard branch (-) Standard branch (-) Standard early cosmology Standard early cosmology 5D late time cosmology 5D late time cosmology Selfaccelerating branch (+) Selfaccelerating branch (+) Standard early cosmology Standard early cosmology Late time acceleration Late time acceleration

13. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 Comparison with Experiment Flat DGP excluded by geometrical probes Flat DGP excluded by geometrical probes Open DGP only marginally worse than flat ΛCDM (1 extra parameter) Open DGP only marginally worse than flat ΛCDM (1 extra parameter) Non-geometrical probes can tell DGP and ΛCDM apart Non-geometrical probes can tell DGP and ΛCDM apart Song, Sawicki, Hu ‘06

14. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 Caveats There is an intrinsic strong coupling in the model There is an intrinsic strong coupling in the model Difficult to compute solutions valid at all scales Difficult to compute solutions valid at all scales Ghosts (negative energy states) present in linear perturbations around the selfaccelerating branch Ghosts (negative energy states) present in linear perturbations around the selfaccelerating branch The model may have problems with a local, causal, unitary UV completion The model may have problems with a local, causal, unitary UV completion Might be solved at the non-linear level Might be solved at the non-linear level Not obvious solution (yet) to the cosmological constant problem 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 Vainshtein ’72; Deffayet, Dvali, Gabadadze, Vainshtein ’01; Gruzinov ’01; Luty, Porrati, Rattazzi ’03; Rubakov ’03

15. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 Let us consider a more general model with a negative bulk cosmological constant and two branes with arbitrary tensions and localized curvature terms 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 We can have (Anti) de Sitter or flat branes at an arbitrary separation Bulk curvature can help understand problems Bulk curvature can help understand problems Generalizations of DGP Bao, Carena, Lykken, Park, Santiago ’05-06

16. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 We can study all the models at once, as a function of the input parameters 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 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 Generalizations of DGP No DGP ghost There is a massless graviton ghost that does not decouple in the limit of an infinite extra dimension Bao, Carena, Lykken, Park, Santiago ’05-06

17. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 Brane with two extra dimensions Brane with two extra dimensions Brane tension does not curve the bulk Brane tension does not curve the bulk Conical singularity that cancels the brane tension Conical singularity that cancels the brane tension Supersymmetry cancels out quantum corrections to the cosmological constant above M SUSY Supersymmetry cancels out quantum corrections to the cosmological constant above M SUSY Supersymmetric Large Extra DimensionS (SLEDS) Aghababaie, Burgess, Parameswaran, Quevedo ’04

18. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 The Model: The Model: 6D Supergravity with two 3-branes 6D Supergravity with two 3-branes Compactification by fluxes with R~0.1 mm Compactification by fluxes with R~0.1 mm Conical singularities at brane locations flat branes Conical singularities at brane locations flat branes SLEDS

19. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 The Model: The Model: 6D Supergravity with two 3-branes 6D Supergravity with two 3-branes Compactification by fluxes with R~0.1 mm Compactification by fluxes with R~0.1 mm Conical singularities at brane locations flat branes Conical singularities at brane locations flat branes SLEDS Most general solution with axial symm. and maximally 4D symm. has flat branes Most general solution with axial symm. and maximally 4D symm. has flat branes Gibbons, Guvens, Pope, 03

20. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 Contribution to low-energy cosmological constant: Contribution to low-energy cosmological constant: Brane tension: SUSY badly broken on the brane Brane tension: SUSY badly broken on the brane Classical bulk contribution: conical singularity Classical bulk contribution: conical singularity Bulk quantum contribution: determined by bulk SUSY Bulk quantum contribution: determined by bulk SUSY SLEDS

21. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 Fundamental explanation of scales Fundamental explanation of scales How to explain 0.1 mm extra dimensions? How to explain 0.1 mm extra dimensions? But relates hierarchy and cosmological constant problems But relates hierarchy and cosmological constant problems Detailed analysis of dynamics of relaxation Detailed analysis of dynamics of relaxation Higher curvature terms Higher curvature terms Thick branes Thick branes Quantum corrections might be too big Quantum corrections might be too big Will be experimentally tested in the near future Will be experimentally tested in the near future Caveats Navarro, Santiago 05 Bostock, Gregory, Navarro, Santiago 04

22. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 Extra dimensions give a new perspective to gravity Extra dimensions give a new perspective to gravity Braneworlds: New freedom to attack old problems Braneworlds: New freedom to attack old problems DGP model: DGP model: Can explain acceleration without a cosmological constant Can explain acceleration without a cosmological constant Strongly coupled: difficult to compute at all scales Strongly coupled: difficult to compute at all scales SLEDS SLEDS Can explain the smallness of the “cosmological constant” Can explain the smallness of the “cosmological constant” Full time-dependent equations difficult to solve Full time-dependent equations difficult to solve Not yet a solution to the CC problem but... Not yet a solution to the CC problem but... Conclusions

23. J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007 It’s difficult to make predictions...... especially about the future Yogi Berra