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 = 0 +  In the fundamental theory, why should 0 be small? Given that 0 is small, why does it stay small as one integrates out physics up to the scales for which 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. Anthropism v. Technical Naturalness Given a small quantity = 0 +  Why can’t 0 cancel  ? Given enough vacua perhaps this cancellation occurs in some. It may only be possible to discuss this problem in those vacua where cancellation occurs.

7. Anthropism v. Technical Naturalness Given a small quantity = 0 +  Why can’t 0 cancel  ? Given enough vacua perhaps this cancellation occurs in some. It may only be possible to discuss this problem in those vacua where cancellation occurs. Possibly, but: Other hierarchies have natural understanding; Leads one to stop thinking about how to solve the problem. Perhaps the 6D case to be presented is more likely than the 4D fine-tuned solution.

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

9. Vacuum Energy & 4D Curvature 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. Arkani-Hamad et al Kachru et al, Carroll & Guica Aghababaie, et al

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

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: There are precisely two extra dimensions at these scales; We are brane bound;

12. 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.

13. 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 M g on the branes; Trickle-down of SUSY breaking to the bulk is:

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

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

16. 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.

17. 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

18. 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)

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

20. 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 Tensions cancel between brane and bulk!! Chen, Luty & Ponton

21. 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 Smooth parts also cancel for supersymmetric theories!! Aghababaie et al.

22. 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 m sb ~ 10 -2 eV Quantum corrections can be right size in absence of m sb 2 M g 2 terms! Lifts flat direction.

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?

24. 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? What Needs Understanding Search for solutions to 6D supergravity: What bulk geometry arises from a given brane configuration?

25. 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? What Needs Understanding Search for solutions to 6D supergravity: What kind of bulk geometry arises from a given pair of branes?

26. 6D Solutions: No Branes Salam Sezgin ansatz: maximal symmetry in 4D and in 2D ds 2 = g  dx  dx + g mn dy m dy n F = f  mn dy m dy n ;  m  = 0

27. 6D Solutions: No Branes Salam Sezgin ansatz: maximal symmetry in 4D and in 2D ds 2 = g  dx  dx + g mn dy m dy n F = f  mn dy m dy n ;  m  = 0 Implies: 1. g  =   2. spherical extra dimensions 3. dilaton stabilization: g 2 e  = 1/r 2

28. 6D Solutions: No Branes Why a flat solution? 80’s: Unit magnetic flux leaves SUSY unbroken…

29. 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!

30. 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

31. 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

32. 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

33. 6D Solutions: Asymptotic forms General near-brane asymptotic behaviour: Solutions take power-law near-brane form as a function of the proper distance, , to the brane Field equations imply ‘Kasner-like’ relations amongst the powers: p -  =  + 3  +  =  2 + 3  2 +  2 + p 2 = 1 Lorentz invariant if:  =  Tolley, CB, Hoover & Aghababaie

34. 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

35. 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 (    ): Static solutions exist for which the time and space parts of the 4D metric vary differently within the bulk; Tolley, CB, Hoover & Aghababaie

36. 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

37. 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

38. 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? What Needs Understanding 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.

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

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

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

44. 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

45. 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;… Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Albrecht, CB, Ravndal & Skordis Potential domination when: Canonical Variables:

46. 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;… Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Albrecht, CB, Ravndal & Skordis log  vs log a Radiation Matter Total Scalar

47. 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;… Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Albrecht, CB, Ravndal & Skordis Radiation Matter Total Scalar w Parameter:  and  w vs log a   ~ 0.7 w ~ – 0.9  m ~ 0.25

48. 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;… Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Albrecht, CB, Ravndal & Skordis  vs log a

49. 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;… Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Albrecht, CB, Ravndal & Skordis log r vs log a

50. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics At small distances: Changes Newton’s Law at range r/2  ~ 1  m. At large distances Scalar-tensor theory out to distances of order H 0.

51. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics At small distances: Changes Newton’s Law at range r/2  ~ 1  m. At large distances Scalar-tensor theory out to distances of order H 0.

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

53. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Not the MSSM! No superpartners Bulk scale bounded by astrophysics M g ~ 10 TeV Many channels for losing energy to KK modes Scalars, fermions, vectors live in the bulk Dimensionless coupling! O(0.1-0.001) from loops Azuelos, Beauchemin & CB

54. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Not the MSSM! No superpartners Bulk scale bounded by astrophysics M g ~ 10 TeV Many channels for losing energy to KK modes Scalars, fermions, vectors live in the bulk Dimensionless coupling! O(0.1-0.001) from loops Azuelos, Beauchemin & CB

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

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

57. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics SLED predicts there are 6D massless fermions in the bulk, as well as their properties Massless, chiral, etc. Masses and mixings can be chosen to agree with oscillation data. Most difficult: bounds on resonant SN oscillilations. Matias, CB & London

58. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics SLED predicts there are 6D massless fermions in the bulk, as well as their properties Massless, chiral, etc. Masses and mixings can be naturally achieved which agree with data! Sterile bounds; oscillation experiments; Matias, CB & London 6D supergravities have many bulk fermions: Gravity: (g mn,  m, B mn, ,  ) Gauge: (A m, ) Hyper: ( ,  ) Bulk couplings dictated by supersymmetry In particular: 6D fermion masses must vanish Back-reaction removes KK zero modes eg: boundary condition due to conical defect at brane position

59. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics SLED predicts there are 6D massless fermions in the bulk, as well as their properties Massless, chiral, etc. Masses and mixings can be naturally achieved which agree with data! Sterile bounds; oscillation experiments; Matias, CB & London Dimensionful coupling ~ 1/M g

60. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics SLED predicts there are 6D massless fermions in the bulk, as well as their properties Massless, chiral, etc. Masses and mixings can be naturally achieved which agree with data! Sterile bounds; oscillation experiments; Matias, CB & London Dimensionful coupling ~ 1/M g SUSY keeps N massless in bulk; Natural mixing with Goldstino on branes; Chirality in extra dimensions provides natural L;

61. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics SLED predicts there are 6D massless fermions in the bulk, as well as their properties Massless, chiral, etc. Masses and mixings can be naturally achieved which agree with data! Sterile bounds; oscillation experiments; Matias, CB & London Dimensionful coupling! ~ 1/M g

62. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics SLED predicts there are 6D massless fermions in the bulk, as well as their properties Massless, chiral, etc. Masses and mixings can be naturally achieved which agree with data! Sterile bounds; oscillation experiments; Matias, CB & London t Dimensionful coupling! ~ 1/M g Constrained by bounds on sterile neutrino emission Require observed masses and large mixing.

63. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics SLED predicts there are 6D massless fermions in the bulk, as well as their properties Massless, chiral, etc. Masses and mixings can be naturally achieved which agree with data! Sterile bounds; oscillation experiments; Matias, CB & London t Dimensionful coupling! ~ 1/M g Constrained by bounds on sterile neutrino emission Require observed masses and large mixing. Bounds on sterile neutrinos easiest to satisfy if g < 10 -4. Degenerate perturbation theory implies massless states strongly mix even if g is small. This is a problem if there are massless KK modes. This is good for 3 observed flavours. Brane back-reaction can remove the KK zero mode for fermions.

64. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics SLED predicts there are 6D massless fermions in the bulk, as well as their properties Massless, chiral, etc. Masses and mixings can be naturally achieved which agree with data! Sterile bounds; oscillation experiments; Matias, CB & London Imagine lepton- breaking terms are suppressed. Possibly generated by loops in running to low energies from M g. Acquire desired masses and mixings with a mild hierarchy for g’/g and  ’/  Build in approximate L e – L  – L , and Z 2 symmetries. S ~ M g r

65. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics SLED predicts there are 6D massless fermions in the bulk, as well as their properties Massless, chiral, etc. Masses and mixings can be naturally achieved which agree with data! Sterile bounds; oscillation experiments; Matias, CB & London 1 massless state 2 next- lightest states have strong overlap with brane. Inverted hierarchy. Massive KK states mix weakly.

66. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics SLED predicts there are 6D massless fermions in the bulk, as well as their properties Massless, chiral, etc. Masses and mixings can be naturally achieved which agree with data! Sterile bounds; oscillation experiments; Matias, CB & London 1 massless state 2 next- lightest states have strong overlap with brane. Inverted hierarchy. Massive KK states mix weakly. Worrisome: once we choose g ~ 10 -4, good masses for the light states require:  S = k ~ 1/g Must get this from a real compactification.

67. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics SLED predicts there are 6D massless fermions in the bulk, as well as their properties Massless, chiral, etc. Masses and mixings can be naturally achieved which agree with data! Sterile bounds; oscillation experiments; Matias, CB & London Lightest 3 states can have acceptable 3- flavour mixings. Active sterile mixings can satisfy incoherent bounds provided g ~ 10 -4 or less (  i ~ g/c i ). 2

68. Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Energy loss into extra dimensions is close to existing bounds Supernova, red-giant stars,… Scalar-tensor form for gravity may have astrophysical implications. Binary pulsars;…

69. The Good News Technically natural solution to the cosmological constant problem may be possible. Unconventional realization of weak-scale supersymmetry breaking. Enormously predictive, with many observational consequences. Cosmology at Colliders! Tests of gravity…

70. Current Worries Technically natural brane choices Runaway solutions and initial conditions. What controls scalar-tensor bounds. How contrived is post-BBN cosmology? (Robustness to initial conditions, etc) Large-extra dimensional pre-BBN cosmology? Dynamics of volume and warping. Connection to string theory?