Gravity and Extra Dimensions

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. 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

3. 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

4. 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

5. 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

6. SM ED Bulk Gravity Braneworld Gravity • Braneworld gravity allows many new possibilities J. Santiago, Gravity and Extra Dimensions

7. 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

8. 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

9. Extra-dimensional takes at the Cosmological Constant problem J. Santiago, Gravity and Extra Dimensions

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. It’s difficult to make predictions ... ... especially about the future Yogi Berra J. Santiago, Gravity and Extra Dimensions