The Cosmological Constant on the Brane

1. The Cosmological Constant on the Brane New Approaches to Naturalness Cliff Burgess

2. Partners in Crime CC Problem: Y. Aghababaie, J. Cline, C. de Rham, H. Firouzjahi, D. Hoover, S. Parameswaran, F. Quevedo, G. Tasinato, A. Tolley, I. Zavala Phenomenology: G. Azuelos, P.-H. Beauchemin, J. Matias, F. Quevedo Cosmology: A. Albrecht, F. Ravndal, C. Skordis

3. The Plan • Naturalness and Cosmology • Why naturalness is an important criterion • 4D Dark Energy from 6D Supergravity • Changing how the vacuum energy gravitates. • Supersymmetric Large Extra Dimensions (SLED) • Have we been MSLED? • Cosmology; Colliders; Newton’s Law; Neutrino Oscillations…

4. Naturalness and Dark Energy • Why doesn’t the electron contribute too large a zero-point energy to the cosmological constant?

5. Technical Naturalness Given a small quantity l =l0 + dl: In the fundamental theory, why should l0 be small? Given that l0 is small, why does it stay small as one integrates out physics up to the scales for which l is measured? This may have to wait until we know the fundamental theory. This is serious because it involves physics we think we understand…

6. Scales How can these scales be changed to reduce the vacuum energy’s gravity? These scales are natural using standard 4D arguments.

7. Vacuum Energy & 4D Curvature Arkani-Hamad et al Kachru et al, Carroll & Guica Aghababaie, et al • In 4D a Lorentz-invariant vacuum energy necessarily gravitates like a cosmological constant. • In higher dimensions a 4D vacuum energy on a brane can curve the extra dimensions instead of the observed 4 dimensions.

8. The SLED Proposal Suppose physics is extra-dimensional above the 10-2 eV scale. Suppose the physics of the bulk is supersymmetric.

9. The SLED Proposal Suppose physics is extra-dimensional above the 10-2 eV scale. Suppose the physics of the bulk is supersymmetric. Experimentally possible: There are precisely two extra dimensions at these scales; We are brane bound;

10. The SLED Proposal Suppose physics is extra-dimensional above the 10-2 eV scale. Suppose the physics of the bulk is supersymmetric. Experimentally possible: There are precisely two extra dimensions at these scales; We are brane bound; The 6D gravity scale is in the TeV region.

11. The SLED Proposal Suppose physics is extra-dimensional above the 10-2 eV scale. Suppose the physics of the bulk is supersymmetric. Experimentally possible provided: SUSY breaks at scale Mg on the branes; Trickle-down of SUSY breaking to the bulk is:

12. Scales Naturalness for these scales must be rethought in 6D. These scales are natural using standard 4D arguments.

13. The CC Problem in 6D The 6D CC Integrate out brane physics Integrate out bulk physics Classical contribution Quantum corrections

14. The CC Problem in 6D The 6D CC Integrate out brane physics Integrate out bulk physics Classical contribution Quantum corrections Several 6D SUGRAs are known, including chiral and non-chiral variants. None have a 6D CC.

15. The CC Problem in 6D The 6D CC Integrate out brane physics Integrate out bulk physics Classical contribution Quantum corrections Several 6D SUGRAs are known, including chiral and non-chiral variants. None have a 6D CC. Nishino & Sezgin

16. The CC Problem in 6D The 6D CC Integrate out brane physics Integrate out bulk physics Classical contribution Quantum corrections Generates large 4D vacuum energy This energy is localized in the extra dimensions (plus higher-derivatives)

17. The CC Problem in 6D The 6D CC Integrate out brane physics Integrate out bulk physics Classical contribution Quantum corrections Solve classical equations in presence of branes Plug back into action

18. The CC Problem in 6D The 6D CC Integrate out brane physics Integrate out bulk physics Classical contribution Quantum corrections Solve classical equations in presence of branes Plug back into action Chen, Luty & Ponton Tensions cancel between brane and bulk!!

19. The CC Problem in 6D The 6D CC Integrate out brane physics Integrate out bulk physics Classical contribution Quantum corrections Solve classical equations in presence of branes Plug back into action Aghababaie et al. Smooth parts also cancel for supersymmetric theories!!

20. The CC Problem in 6D The 6D CC Integrate out brane physics Integrate out bulk physics Classical contribution Quantum corrections Bulk is a supersymmetric theory with msb ~ 10-2 eV Quantum corrections can be right size in absence of msb2 Mg2 terms! Lifts flat direction.

21. What Needs Understanding Classical part of the argument: What choices must be made to ensure 4D flatness? Quantum part of the argument: Are these choices stable against renormalization?

22. What Needs Understanding Classical part of the argument: What choices must be made to ensure 4D flatness? Quantum part of the argument: Are these choices stable against renormalization? Search for solutions to 6D supergravity: What bulk geometry arises from a given brane configuration?

23. What Needs Understanding Classical part of the argument: What choices must be made to ensure 4D flatness? Quantum part of the argument: Are these choices stable against renormalization? Search for solutions to 6D supergravity: What kind of bulk geometry arises from a given pair of branes?

24. 6D Solutions: No Branes Salam Sezginansatz: maximal symmetry in 4D and in 2D ds2 = gmn dxm dxn + gmn dym dyn F = f emn dym dyn ; ¶mf = 0

25. 6D Solutions: No Branes Salam Sezginansatz: maximal symmetry in 4D and in 2D ds2 = gmn dxm dxn + gmn dym dyn F = f emn dym dyn ; ¶mf = 0 Implies: 1. gmn = hmn 2. spherical extra dimensions 3. dilaton stabilization: g2 ef = 1/r2

26. 6D Solutions: No Branes Why a flat solution? 80’s: Unit magnetic flux leaves SUSY unbroken…

27. 6D Solutions: No Branes Why a flat solution? 80’s: Unit magnetic flux leaves SUSY unbroken… …but: turns out to be 4D flat for higher fluxes as well!

28. 6D Solutions: Rugby Balls Can include branes: Cut-and-paste solutions have equal-sized conical singularities at both poles; Interpret singularity as due to back reaction of branes located at this position Solutions break supersymmetry Aghababaie, CB, Parameswaran & Quevedo

29. 6D Solutions: Conical Singularities General solutions with two conical singularities: Unequal conical defects lead to warped geometries in the bulk; All such (static) solutions have flat 4D geometries Gibbons, Guven & Pope Aghababaie, CB, Cline, Firouzjahi, Parameswaran, Quevedo Tasinato & Zavala

30. 6D Solutions: GGP solutions General solutions with flat 4D geometry: Solutions need not have purely conical singularities at brane positions; Non-conical singularities arise when the dilaton diverges near the branes Gibbons, Guven & Pope

31. 6D Solutions: Asymptotic forms General near-brane asymptotic behaviour: Solutions take power-law near-brane form as a function of the proper distance, r, to the brane Field equations imply ‘Kasner-like’ relations amongst the powers: p - g = w + 3 a + b = w2 + 3 a2 + b2 + p2 = 1 Lorentz invariant if: w = a Tolley, CB, Hoover & Aghababaie

32. 6D Solutions: Brane matching Near-brane asymptotics and brane properties: Powers may be related to averaged conserved currents if the singular behaviour is regulated using a ‘thick brane’ Navarro & Santiago Tolley, CB, de Rham & Hoover

33. 6D Solutions: Other static solutions Solutions with dS and AdS 4D geometry: Asymptotic form at one brane dictated by that at the other brane; Solutions cannot have purely conical singularities at both brane positions; Static Lorentz-breaking solutions (a¹w): Static solutions exist for which the time and space parts of the 4D metric vary differently within the bulk; Tolley, CB, Hoover & Aghababaie

34. 6D Solutions: Time-dependence Linearized perturbations Explicit solutions are possible for conical geometries in terms of Hypergeometric functions: Solutions are marginally stable, if the perturbations are not too singular at the brane positions; Nonlinear Plane-Wave Solutions: Describe eg passage of bubble-nucleation wall along the brane; Tolley, CB, de Rham & Hoover

35. 6D Solutions: Scaling solutions A broad class of exact scaling solutions Exact time-dependent solutions are possible subject to the assumption of a scaling ansatz: Likely to describe the late-time attractor behaviour of time dependent evolution; Most of these solutions describe rapid runaways with rapidly growing or shrinking dimensions. Tolley, CB, de Rham & Hoover Copeland & Seto

36. What Needs Understanding Classical part of the argument: What choices must be made to ensure 4Dflatness? Quantum part of theargument: Are these choices stable against renormalization? When both branes are conical all solutions have 4D minkowski geometry. Conical singularities require vanishing dilaton coupling to branes. Brane loops cannot generate dilaton couplings from scratch. Bulk loops are SUSY suppressed.

37. What About Weinberg’s Theorem? • Weinberg has a general objection to self-tuning mechanisms for solving the cosmological constant problem.

38. What About Weinberg’s Theorem? • Weinberg has a general objection to self-tuning mechanisms for solving the cosmological constant problem.

39. What About Weinberg’s Theorem? • Weinberg has a general objection to self-tuning mechanisms for solving the cosmological constant problem.

40. What About Weinberg’s Theorem? • Weinberg has a general objection to self-tuning mechanisms for solving the cosmological constant problem.

41. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics

42. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Quantum vacuum energy lifts flat direction. Specific types of scalar interactions are predicted. Includes the Albrecht-Skordis type of potential Preliminary studies indicate it is possible to have viable cosmology: Changing G; BBN;… Albrecht, CB, Ravndal & Skordis Kainulainen & Sunhede

43. Observational Consequences Quantum vacuum energy lifts flat direction. Specific types of scalar interactions are predicted. Includes the Albrecht-Skordis type of potential Preliminary studies indicate it is possible to have viable cosmology: Changing G; BBN;… Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Albrecht, CB, Ravndal & Skordis Potential domination when: Canonical Variables:

44. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Albrecht, CB, Ravndal & Skordis Radiation Matter Total Scalar • Quantum vacuum energy lifts flat direction. • Specific types of scalar interactions are predicted. • Includes the Albrecht-Skordis type of potential • Preliminary studies indicate it is possible to have viable cosmology: • Changing G; BBN;… log rvs log a

45. Observational Consequences Quantum vacuum energy lifts flat direction. Specific types of scalar interactions are predicted. Includes the Albrecht-Skordis type of potential Preliminary studies indicate it is possible to have viable cosmology: Changing G; BBN;… Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Albrecht, CB, Ravndal & Skordis • L ~ 0.7 • m ~ 0.25 • andw vs log a Radiation Matter Total Scalar w Parameter: w ~ – 0.9

46. Observational Consequences Quantum vacuum energy lifts flat direction. Specific types of scalar interactions are predicted. Includes the Albrecht-Skordis type of potential Preliminary studies indicate it is possible to have viable cosmology: Changing G; BBN;… Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Albrecht, CB, Ravndal & Skordis avs log a

47. Observational Consequences Quantum vacuum energy lifts flat direction. Specific types of scalar interactions are predicted. Includes the Albrecht-Skordis type of potential Preliminary studies indicate it is possible to have viable cosmology: Changing G; BBN;… Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Albrecht, CB, Ravndal & Skordis log rvs log a

48. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics At small distances: Changes Newton’s Law at range r/2p ~ 1 mm. At large distances Scalar-tensor theory out to distances of order H0.

49. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics At small distances: Changes Newton’s Law at range r/2p ~ 1 mm. At large distances Scalar-tensor theory out to distances of order H0.

50. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Not the MSSM! No superpartners Bulk scale bounded by astrophysics Mg ~ 10 TeV Many channels for losing energy to KK modes Scalars, fermions, vectors live in the bulk