1. Budapest 2007 Extra Dimensions and the Cosmological Constant Problem Cliff Burgess

2. Budapest 2007 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. Budapest 2007 The Plan The Cosmological Constant problem Technical Naturalness in Crisis How extra dimensions might help Changing how the vacuum energy gravitates Making things concrete 6 dimensions and supersymmetry Prognosis Technical worries Observational tests

4. Budapest 2007 Time to Put Up or Shut Up: Technical Naturalness has been our best guide to guessing the physics beyond the Standard Model. Naturalness is the motivation for all the main alternatives: Supersymmetry, Composite Models, Extra Dimensions. The cosmological constant problem throws the validity of naturalness arguments into doubt. Why buy naturalness at the weak scale and not 10 -3 eV? Cosmology alone cannot distinguish amongst the various models of Dark Energy. The features required by cosmology are difficult to sensibly embed into a fundamental microscopic theory.

5. Budapest 2007 Naturalness Ideas for what lies beyond the Standard Model are largely driven by ‘technical naturalness’. Motivated by belief that SM is an effective field theory. + dimensionless

6. Budapest 2007 Naturalness Ideas for what lies beyond the Standard Model are largely driven by ‘technical naturalness’. Motivated by belief that SM is an effective field theory. + dimensionless BUT: effective theory can be defined at many scales Hierarchy Problem: These must cancel to 20 digits!!

7. Budapest 2007 Naturalness Ideas for what lies beyond the Standard Model are largely driven by ‘technical naturalness’. Motivated by belief that SM is an effective field theory. + dimensionless Hierarchy problem: Since the largest mass dominates, why isn’t m ~ M GUT or M p ?? Three approaches to solve the Hierarchy problem: Compositeness: H is not fundamental at energies E À M w Supersymmetry: there are new particles at E À M w and a symmetry which ensures cancellations so m 2 ~ M B 2 – M F 2 Extra Dimensions: the fundamental scale is much smaller than M p, much as G F -1/2 > M w

8. Budapest 2007 Naturalness in Crisis Ideas for what lies beyond the Standard Model are largely driven by ‘technical naturalness’. Motivated by belief that SM is an effective field theory. The Standard Model’s dirty secret: there are really two unnaturally small terms. + dimensionless

9. Budapest 2007 Naturalness in Crisis Ideas for what lies beyond the Standard Model are largely driven by ‘technical naturalness’. Motivated by belief that SM is an effective field theory. + dimensionless Can apply same argument to scales between TeV and sub-eV scales. Cosmological Constant Problem: Must cancel to 32 decimal places!!

10. Budapest 2007 Naturalness in Crisis Ideas for what lies beyond the Standard Model are largely driven by ‘technical naturalness’. Motivated by belief that SM is an effective field theory. The Standard Model’s dirty secret: there are really two unnaturally small terms. + dimensionless Harder than the Hierarchy problem: Integrating out the electron already gives too large a contribution!!

11. Budapest 2007 Naturalness in Crisis Dark energy vs vacuum energy Why must the vacuum energy be large? Seek to change properties of low-energy particles (like the electron) so that their zero-point energy does not gravitate, even though quantum effects do gravitate in atoms! Why this? But not this?

12. Budapest 2007 Naturalness in Crisis Ideas for what lies beyond the Standard Model are largely driven by ‘technical naturalness’. Motivated by belief that SM is an effective field theory. + dimensionless Cosmological constant problem: Why is  ~ 10 -3 eV rather than m e, M w, M GUT or M p ? Approaches to solve the Hierarchy problem at  ~ 10 -2 eV? Compositeness: graviton is not fundamental at energies E À  Supersymmetry: there are new particles at E À  and a symmetry which ensures cancellations so  2 ~ M B 2 – M F 2 Extra Dimensions: the fundamental scale is much smaller than M p ??

13. Budapest 2007 The Plan The Cosmological Constant problem Technical Naturalness in Crisis How extra dimensions might help Changing how the vacuum energy gravitates Making things concrete 6 dimensions and supersymmetry Prognosis Technical worries Observational tests

14. Budapest 2007 How Extra Dimensions Help 4D CC vs 4D vacuum energy Branes and scales

15. Budapest 2007 4D CC vs 4D vacuum energy Branes and scales How Extra Dimensions Help A cosmological constant is not distinguishable* from a Lorentz invariant vacuum energy vs * in 4 dimensions…

16. Budapest 2007 4D CC vs 4D vacuum energy Branes and scales How Extra Dimensions Help In higher dimensions a 4D vacuum energy, if localized in the extra dimensions, can curve the extra dimensions instead of the observed four. Chen, Luty & Ponton Arkani-Hamad et al Kachru et al, Carroll & Guica Aghababaie, et al

17. Budapest 2007 4D CC vs 4D vacuum energy Branes and scales How Extra Dimensions Help These scales are natural using standard 4D arguments. Extra dimensions could start here, if there are only two of them. Arkani Hamed, Dvali, Dimopoulos

18. Budapest 2007 4D CC vs 4D vacuum energy Branes and scales How Extra Dimensions Help Only gravity gets modified over the most dangerous distance scales! Must rethink how the vacuum gravitates in 6D for these scales. SM interactions do not change at all!

19. Budapest 2007 The Plan The Cosmological Constant problem Naturalness in Crisis How extra dimensions might help Changing how the vacuum energy gravitates Making things concrete 6 dimensions and supersymmetry Prognosis Technical worries Observational tests

20. Budapest 2007 The SLED Proposal Suppose physics is extra-dimensional above the 10 -2 eV scale. Suppose the physics of the bulk is supersymmetric. Aghababaie, CB, Parameswaran & Quevedo

21. Budapest 2007 The SLED Proposal Suppose physics is extra-dimensional above the 10 -2 eV scale. Suppose the physics of the bulk is supersymmetric. 6D gravity scale: M g ~ 10 TeV KK scale: 1/r ~ 10 -2 eV Planck scale: M p ~ M g 2 r Arkani-Hamad, Dimopoulos & Dvali

22. Budapest 2007 Suppose physics is extra-dimensional above the 10 -2 eV scale. Suppose the physics of the bulk is supersymmetric. The SLED Proposal 6D gravity scale: M g ~ 10 TeV KK scale: 1/r ~ 10 -2 eV Planck scale: M p ~ M g 2 r Choose bulk to be supersymmetric (no 6D CC allowed) Nishino & Sezgin

23. Budapest 2007 Suppose physics is extra-dimensional above the 10 -2 eV scale. Suppose the physics of the bulk is supersymmetric. The SLED Proposal 6D gravity scale: M g ~ 10 TeV KK scale: 1/r ~ 10 -2 eV Planck scale: M p ~ M g 2 r SUSY Breaking on brane: TeV in bulk: M g 2 /M p ~1/r

24. Budapest 2007 The SLED Proposal 4D graviton Particle Spectrum: 4D scalar: e  r 2 ~ const SM on brane – no partners Many KK modes in bulk

25. Budapest 2007 The SLED Proposal 4D graviton Particle Spectrum: 4D scalar: e  r 2 ~ const SM on brane – no partners Many KK modes in bulk Classical flat direction due to a scale invariance of the classical equations NOT self-tuning: response to a kick is runaway along flat direction.

26. Budapest 2007 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?

27. Budapest 2007 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? What is special about the ones which are 4D flat?

28. Budapest 2007 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? What is special about the ones which are 4D flat?

29. Budapest 2007 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? What is special about the ones which are 4D flat? Chiral gauged supergravity chosen to allow extra dimensions topology of a sphere (only positive tensions):

30. Budapest 2007 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 Many classes of axially symmetric solutions known Up to two singularities, corresponding to presence of brane sources Brane sources characterized by: Asymptotic near-brane behaviour is related to properties of T(  ). dT/d  nonzero implies curvature singularity

31. Budapest 2007 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 Static solutions having only conical singularities are all 4D flatsolutions Unequal defect angles imply warping. Flat solutions with curvature singularities exist.solutions Static solutions exist which are 4D dS.solutions Runaways are generic. Runaways Tolley, CB, Hoover & Aghababaie Tolley, CB, de Rham & Hoover CB, Hoover & Tasinato Gibbons, Guvens & Pope

32. Budapest 2007 4D CC vs 4D vacuum energy Branes and scales What Needs Understanding Most general 4D flat solutions to chiral 6D supergravity, without matter fields. 3 nonzero gives curvature singularities at branes Gibbons, Guven & Pope

33. Budapest 2007 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

34. Budapest 2007 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

35. Budapest 2007 6D Solutions: No Branes Why a flat solution? 80’s: Unit magnetic flux leaves SUSY unbroken…

36. Budapest 2007 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!

37. Budapest 2007 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

38. Budapest 2007 6D Solutions: Conical Singularities General solns with two conical singularities: Unequal defects have warped geometries in the bulk; Conical singularities correspond to absence of brane coupling to 6D dilaton (and preserve bulk scale invariance) All such (static) solutions have flat 4D geometries Gibbons, Guven & Pope Aghababaie, CB, Cline, Firouzjahi, Parameswaran, Quevedo Tasinato & Zavala

39. Budapest 2007 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

40. Budapest 2007 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

41. Budapest 2007 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

42. Budapest 2007 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

43. Budapest 2007 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; Cline & Vinet Tolley, CB, de Rham & Hoover Lee & Papazoglou

44. Budapest 2007 6D Solutions: Time-dependence Nonlinear Plane-Wave Solutions: Describe eg passage of bubble-nucleation wall along the brane; Black Hole Solutions: Conical defects threaded through bulk black holes Tolley et al Kaloper et al

45. Budapest 2007 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

46. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Quantum part of the argument: Are these choices stable against renormalization? So far so good, but not yet complete Brane loops cannot generate dilaton couplings if these are not initially present Bulk loops can generate such couplings, but are suppressed by 6D supersymmetry

47. Budapest 2007 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?

48. Budapest 2007 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? When both branes have conical singularities all static solutions have 4D minkowski geometry.

49. Budapest 2007 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? When both branes have conical singularities all static solutions have 4D minkowski geometry. Conical singularities require vanishing dilaton coupling to branes (and hence scale invariant)

50. Budapest 2007 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? When both branes have conical singularities all static solutions have 4D minkowski geometry. Conical singularities require vanishing dilaton coupling to branes (and hence scale invariant) Brane loops on their own cannot generate dilaton couplings from scratch.

51. Budapest 2007 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? When both branes have conical singularities all static solutions have 4D minkowski geometry. Conical singularities require vanishing dilaton coupling to branes (and hence scale invariant) Brane loops on their own cannot generate dilaton couplings from scratch. Bulk loops can generate brane-dilaton coupling but TeV scale modes are suppressed at one loop by 6D supersymmetry

52. Budapest 2007 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? When both branes have conical singularities all static solutions have 4D minkowski geometry. Conical singularities require vanishing dilaton coupling to branes (and hence scale invariant) Brane loops on their own cannot generate dilaton couplings from scratch. Bulk loops can generate brane-dilaton coupling but TeV scale modes are suppressed at one loop by 6D supersymmetry Each bulk loop costs power of e  ~ 1/r 2 and so only a few loops must be checked…..

53. Budapest 2007 The Plan The Cosmological Constant problem Why is it so hard? How extra dimensions might help Changing how the vacuum energy gravitates Making things concrete 6 dimensions and supersymmetry Prognosis Technical worries Observational tests

54. Budapest 2007 Prognosis Theoretical worries Observational tests

55. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars

56. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars

57. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars 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?

58. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Classical part of the argument: What choices must be made to ensure 4D flatness? Now understand how 2 extra dimensions respond to presence of 2 branes having arbitrary couplings. Not all are flat in 4D, but all of those having only conical singularities are flat. (Conical singularities correspond to absence of dilaton couplings to branes) Tolley, CB, Hoover & Aghababaie Tolley, CB, de Rham & Hoover CB, Hoover & Tasinato

59. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Quantum part of the argument: Are these choices stable against renormalization? So far so good, but not yet complete Brane loops cannot generate dilaton couplings if these are not initially present Bulk loops can generate such couplings, but are suppressed by 6D supersymmetry

60. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars

61. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Most brane properties and initial conditions do not lead to anything like the universe we see around us. For many choices the extra dimensions implode or expand to infinite size. Albrecht, CB, Ravndal, Skordis Tolley, CB, Hoover & Aghababaie Tolley, CB, de Rham & Hoover

62. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Most brane properties and initial conditions do not lead to anything like the universe we see around us. For many choices the extra dimensions implode or expand to infinite size. Initial condition problem: much like the Hot Big Bang, possibly understood by reference to earlier epochs of cosmology (eg: inflation) Albrecht, CB, Ravndal, Skordis Tolley, CB, Hoover & Aghababaie Tolley, CB, de Rham & Hoover

63. Budapest 2007 Prognosis Theoretical worries Observational tests

64. Budapest 2007 Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics? And more! SUSY broken at the TeV scale, but not the MSSM!

65. Budapest 2007 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

66. Budapest 2007 Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Can there be observable signals if M g ~ 10 TeV? Must hit new states before E ~ M g. Eg: string and KK states have M KK < M s < M g

67. Budapest 2007 Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Can there be observable signals if M g ~ 10 TeV? Must hit new states before E ~ M g. Eg: string and KK states have M KK < M s < M g Dimensionless couplings to bulk scalars are unsuppressed by M g

68. Budapest 2007 Summary It is too early to abandon naturalness as a fundamental criterion! It is the interplay between cosmological phenomenology and microscopic constraints which will make it possible to solve the Dark Energy problem. Technical naturalness provides a crucial clue. 6D brane-worlds allow progress on technical naturalness: Vacuum energy not equivalent to curved 4D Are ‘Flat’ choices stable against renormalization? Tuned initial conditions Much like for the Hot Big Bang Model. Enormously predictive, with many observational consequences. Cosmology at Colliders! Tests of gravity…

69. Budapest 2007 Detailed Worries and Observations ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Quintessence cosmology Modifications to gravity Collider physics Neutrino physics?

70. Budapest 2007 Backup slides

71. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars

72. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Classical flat direction corresponding to combination of radius and dilaton: e  r 2 = constant. Loops lift this flat direction, and in so doing give dynamics to  and r. Salam & Sezgin

73. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Potential domination when: Canonical Variables: Kantowski & Milton Albrecht, CB, Ravndal, Skordis CB & Hoover Ghilencea, Hoover, CB & Quevedo

74. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Potential domination when: Canonical Variables: Albrecht, CB, Ravndal, Skordis Hubble damping can allow potential domination for exponentially large r, even though r is not stabilized.

75. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars

76. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Why isn’t this killed by what killed 5D self-tuning? In 5D models, presence of one brane with nonzero positive tension T 1 implied a singularity in the bulk. Singularity can be interpreted as presence of a second brane whose tension T 2 need be negative. This is a hidden fine tuning: T 1 + T 2 = 0 Nilles et al Cline et al Erlich et al

77. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Why isn’t this killed by what killed 5D self-tuning? In 5D models, presence of one brane with nonzero positive tension T 1 implied a singularity in the bulk. Singularity can be interpreted as presence of a second brane whose tension T 2 need be negative. This is a hidden fine tuning: T 1 + T 2 = 0 Nilles et al Cline et al Erlich et al

78. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Why isn’t this killed by what killed 5D self-tuning? In 5D models, presence of one brane with nonzero positive tension T 1 implied a singularity in the bulk. Singularity can be interpreted as presence of a second brane whose tension T 2 need be negative. This is a hidden fine tuning: T 1 + T 2 = 0 Nilles et al Cline et al Erlich et al 6D analog corresponds to the Euler number topological constraint:

79. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Why isn’t this killed by what killed 5D self-tuning? In 5D models, presence of one brane with nonzero positive tension T 1 implied a singularity in the bulk. Singularity can be interpreted as presence of a second brane whose tension T 2 need be negative. This is a hidden fine tuning: T 1 + T 2 = 0 Nilles et al Cline et al Erlich et al 6D analog corresponds to the Euler number topological constraint: Being topological, this is preserved under renormalization. If  T b nonzero then R becomes nonzero

80. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Weinberg’s No-Go Theorem: Steven Weinberg has a general objection to self-tuning mechanisms for solving the cosmological constant problem that are based on scale invariance

81. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Weinberg’s No-Go Theorem: Steven Weinberg has a general objection to self-tuning mechanisms for solving the cosmological constant problem that are based on scale invariance

82. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Weinberg’s No-Go Theorem: Steven Weinberg has a general objection to self-tuning mechanisms for solving the cosmological constant problem that are based on scale invariance

83. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Nima’s No-Go Argument: One can have a vacuum energy  4 with  greater than the cutoff, provided it is turned on adiabatically. So having extra dimensions with r ~ 1/  does not release one from having to find an intrinsically 4D mechanism.

84. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Nima’s No-Go Argument: One can have a vacuum energy  4 with  greater than the cutoff, provided it is turned on adiabatically. So having extra dimensions with r ~ 1/  does not release one from having to find an intrinsically 4D mechanism. Scale invariance precludes obtaining  greater than the cutoff in an adiabatic way: implies

85. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars

86. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Post BBN: Since r controls Newton’s constant, its motion between BBN and now will cause unacceptably large changes to G.

87. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Post BBN: Since r controls Newton’s constant, its motion between BBN and now will cause unacceptably large changes to G. Even if the kinetic energy associated with r were to be as large as possible at BBN, Hubble damping keeps it from rolling dangerously far between then and now.

88. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Post BBN: Since r controls Newton’s constant, its motion between BBN and now will cause unacceptably large changes to G. Even if the kinetic energy associated with r were to be as large as possible at BBN, Hubble damping keeps it from rolling dangerously far between then and now. log r vs log a

89. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Pre BBN: There are strong bounds on KK modes in models with large extra dimensions from: * their later decays into photons; * their over-closing the Universe; * their light decay products being too abundant at BBN

90. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars Pre BBN: There are strong bounds on KK modes in models with large extra dimensions from: * their later decays into photons; * their over-closing the Universe; * their light decay products being too abundant at BBN Photon bounds can be evaded by having invisible channels; others are model dependent, but eventually must be addressed

91. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars

92. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars A light scalar with mass m ~ H has several generic difficulties: What protects such a small mass from large quantum corrections?

93. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars A light scalar with mass m ~ H has several generic difficulties: What protects such a small mass from large quantum corrections? Given a potential of the form V(r) = c 0 M 4 + c 1 M 2 /r 2 + c 2 /r 4 + … then c 0 = c 1 = 0 ensures both small mass and small dark energy.

94. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars A light scalar with mass m ~ H has several generic difficulties: Isn’t such a light scalar already ruled out by precision tests of GR in the solar system?

95. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars A light scalar with mass m ~ H has several generic difficulties: Isn’t such a light scalar already ruled out by precision tests of GR in the solar system? The same logarithmic corrections which enter the potential can also appear in its matter couplings, making them field dependent and so also time-dependent as  rolls. Can arrange these to be small here & now.

96. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars A light scalar with mass m ~ H has several generic difficulties: Isn’t such a light scalar already ruled out by precision tests of GR in the solar system? The same logarithmic corrections which enter the potential can also appear in its matter couplings, making them field dependent and so also time-dependent as  rolls. Can arrange these to be small here & now.  vs log a

97. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars A light scalar with mass m ~ H has several generic difficulties: Shouldn’t there be strong bounds due to energy losses from red giant stars and supernovae? (Really a bound on LEDs and not on scalars.)

98. Budapest 2007 The Worries ‘Technical Naturalness’ Runaway Behaviour Stabilizing the Extra Dimensions Famous No-Go Arguments Problems with Cosmology Constraints on Light Scalars A light scalar with mass m ~ H has several generic difficulties: Shouldn’t there be strong bounds due to energy losses from red giant stars and supernovae? (Really a bound on LEDs and not on scalars.) Yes, and this is how the scale M ~ 10 TeV for gravity in the extra dimensions is obtained.

99. Budapest 2007 Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics

100. Budapest 2007 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

101. Budapest 2007 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:

102. Budapest 2007 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

103. Budapest 2007 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

104. Budapest 2007 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

105. Budapest 2007 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

106. Budapest 2007 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.

107. Budapest 2007 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.

108. Budapest 2007 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

109. Budapest 2007 Observational Consequences Quintessence cosmology Modifications to gravity Collider physics Neutrino physics Astrophysics Can there be observable signals if M g ~ 10 TeV? Must hit new states before E ~ M g. Eg: string and KK states have M KK < M s < M g Dimensionless couplings to bulk scalars are unsuppressed by M g

110. Budapest 2007 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

111. Budapest 2007 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 Use H decay into , so search for two hard photons plus missing E T.

112. Budapest 2007 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 Standard Model backgrounds

113. Budapest 2007 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

114. Budapest 2007 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 Significance of signal vs cut on missing E T

115. Budapest 2007 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 Possibility of missing-E T cut improves the reach of the search for Higgs through its  channel

116. Budapest 2007 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

117. Budapest 2007 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; 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 Matias, CB

118. Budapest 2007 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; Dimensionful coupling ~ 1/M g Matias, CB

119. Budapest 2007 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; Dimensionful coupling ~ 1/M g SUSY keeps N massless in bulk; Natural mixing with Goldstino on branes; Chirality in extra dimensions provides natural L; Matias, CB

120. Budapest 2007 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; Dimensionful coupling! ~ 1/M g Matias, CB

121. Budapest 2007 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; t Dimensionful coupling! ~ 1/M g Constrained by bounds on sterile neutrino emission Require observed masses and large mixing. Matias, CB

122. Budapest 2007 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; 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 = v < 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. Matias, CB

123. Budapest 2007 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; 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 Matias, CB

124. Budapest 2007 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; 1 massless state 2 next- lightest states have strong overlap with brane. Inverted hierarchy. Massive KK states mix weakly. Matias, CB

125. Budapest 2007 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; 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. Matias, CB

126. Budapest 2007 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; 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 Matias, CB

127. Budapest 2007 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;…