Extra Dimensions and the Cosmological Constant Problem

1
Extra Dimensions and the Cosmological Constant
Problem

• 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

• 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
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
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
Naturalness
BUT effective theory can be defined at many
scales

• 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 These must cancel to 20
digits!!
7
Naturalness

• Three approaches to solve the Hierarchy problem
• Compositeness H is not fundamental at energies
  E À Mw
• Supersymmetry there are new particles at E À Mw
  and a symmetry which ensures cancellations so m2
  MB2 MF2
• Extra Dimensions the fundamental scale is much
  smaller than Mp , much as GF-1/2 gt Mw

• 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 isnt m MGUT or Mp ??
8
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 Models dirty secret there are
  really two unnaturally small terms.

dimensionless
9
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.

Can apply same argument to scales between TeV
and sub-eV scales.
dimensionless
Cosmological Constant Problem Must cancel to 32
decimal places!!
10
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 Models dirty secret there are
  really two unnaturally small terms.

Harder than the Hierarchy problem
Integrating out the electron already gives too
large a contribution!!
dimensionless
11
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
Naturalness in Crisis

• Approaches to solve the Hierarchy problem at m
  10-2 eV?
• Compositeness graviton is not fundamental at
  energies E À m
• Supersymmetry there are new particles at E À m
  and a symmetry which ensures cancellations so m2
  MB2 MF2
• Extra Dimensions the fundamental scale is much
  smaller than Mp

• 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
m 10-3 eV rather than me , Mw , MGUT or Mp?
13
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
How Extra Dimensions Help

• 4D CC vs 4D vacuum energy
• Branes and scales

15
How Extra Dimensions Help

• 4D CC vs 4D vacuum energy
• Branes and scales

A cosmological constant is not distinguishable
from a Lorentz invariant vacuum energy vs
in 4 dimensions
16
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.

• 4D CC vs 4D vacuum energy
• Branes and scales

Chen, Luty Ponton Arkani-Hamad et al Kachru et
al, Carroll Guica Aghababaie, et al
17
How Extra Dimensions Help
Arkani Hamed, Dvali, Dimopoulos
Extra dimensions could start here, if there
are only two of them.

• 4D CC vs 4D vacuum energy
• Branes and scales

These scales are natural using standard 4D
arguments.
18
How Extra Dimensions Help
Must rethink how the vacuum gravitates in 6D
for these scales. SM interactions do not
change at all!

• 4D CC vs 4D vacuum energy
• Branes and scales

Only gravity gets modified over the most
dangerous distance scales!
19
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
The SLED Proposal
Aghababaie, CB, Parameswaran Quevedo

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

21
The SLED Proposal
Arkani-Hamad, Dimopoulos Dvali

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

• 6D gravity scale Mg 10 TeV
• KK scale 1/r 10-2 eV
• Planck scale Mp Mg2 r

22
The SLED Proposal
Nishino Sezgin

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

• 6D gravity scale Mg 10 TeV
• KK scale 1/r 10-2 eV
• Planck scale Mp Mg2 r
• Choose bulk to be supersymmetric (no 6D CC
  allowed)

23
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 Mg 10 TeV
• KK scale 1/r 10-2 eV
• Planck scale Mp Mg2 r
• SUSY Breaking on brane TeV in bulk Mg2/Mp
  1/r

24
The SLED Proposal
Particle Spectrum
SM on brane no partners Many KK modes
in bulk
4D scalar ef r2 const
4D graviton
25
The SLED Proposal
Particle Spectrum
Classical flat direction due to a scale
invariance of the classical equations NOT
self-tuning response to a kick is runaway along
flat direction.
SM on brane no partners Many KK modes
in bulk
4D scalar ef r2 const
4D graviton
26
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
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?

• 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?

28
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?

• 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?

29
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?

• 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?

• Chiral gauged supergravity chosen to allow extra
  dimensions topology of a sphere (only positive
  tensions)

30
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(f).
• dT/df nonzero implies curvature singularity

• 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?

31
What Needs Understanding

• Static solutions having only conical
  singularities are all 4D flat
• Unequal defect angles imply warping.
• Flat solutions with curvature singularities
  exist.
• Static solutions exist which are 4D dS.
• Runaways are generic.

• 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?

Gibbons, Guvens Pope
Tolley, CB, Hoover Aghababaie Tolley, CB, de
Rham Hoover CB, Hoover Tasinato
32
What Needs Understanding
Gibbons, Guven Pope

• 4D CC vs 4D vacuum energy
• Branes and scales

• Most general 4D flat solutions to chiral 6D
  supergravity, without matter fields.
• l3 nonzero gives curvature singularities at
  branes

33
6D Solutions No Branes

• Salam Sezgin ansatz maximal symmetry in 4D
  and in 2D
• ds2 gmn dxm dxn gmn dym dyn
• F f emn dym dyn m f 0

34
6D Solutions No Branes

• Salam Sezgin ansatz maximal symmetry in 4D
  and in 2D
• ds2 gmn dxm dxn gmn dym dyn
• F f emn dym dyn m f 0
• Implies
• 1. gmn hmn
• 2. spherical extra dimensions
• 3. dilaton stabilization
• g2 ef 1/r2

35
6D Solutions No Branes

• Why a flat solution?
• 80s Unit magnetic flux leaves SUSY
• unbroken

36
6D Solutions No Branes

• Why a flat solution?
• 80s Unit magnetic flux leaves SUSY
• unbroken
• but turns out to be 4D flat for
  higher fluxes as well!

37
6D Solutions Rugby Balls
Aghababaie, CB, Parameswaran Quevedo

• 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

38
6D Solutions Conical Singularities
Gibbons, Guven Pope Aghababaie, CB, Cline,
Firouzjahi, Parameswaran, Quevedo Tasinato
Zavala

• 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

39
6D Solutions GGP solutions
Gibbons, Guven Pope

• 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

40
6D Solutions Asymptotic forms
Tolley, CB, Hoover Aghababaie

• 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

41
6D Solutions Brane matching
Navarro Santiago Tolley, CB, de Rham Hoover

• Near-brane asymptotics and brane properties
• Powers may be related to averaged conserved
  currents if the singular behaviour is regulated
  using a thick brane

42
6D Solutions Other static solutions
Tolley, CB, Hoover Aghababaie

• 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 (a ¹ w)
• Static solutions exist for which the time and
  space parts of the 4D metric vary differently
  within the bulk

43
6D Solutions Time-dependence
Cline Vinet Tolley, CB, de Rham Hoover Lee
Papazoglou

• 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

44
6D Solutions Time-dependence
Tolley et al Kaloper et al

• Nonlinear Plane-Wave Solutions
• Describe eg passage of bubble-nucleation
  wall along the brane
• Black Hole Solutions
• Conical defects threaded through bulk
  black holes

45
6D Solutions Scaling solutions
Tolley, CB, de Rham Hoover Copeland Seto

• 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.

46
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
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
What Needs Understanding

• When both branes have conical singularities all
  static solutions have 4D minkowski geometry.

• 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?

49
What Needs Understanding

• 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)

• 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?

50
What Needs Understanding

• 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.

• 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?

51
What Needs Understanding

• 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

• 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?

52
What Needs Understanding

• 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 ef 1/r2 and so
  only a few loops must be checked..

• 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?

53
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
Prognosis

• Theoretical worries
• Observational tests

55
The Worries

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

56
The Worries

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

57
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
The Worries
Tolley, CB, Hoover Aghababaie Tolley, CB, de
Rham Hoover CB, Hoover Tasinato

• 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)

59
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
The Worries

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

61
The Worries
Albrecht, CB, Ravndal, Skordis Tolley, CB,
Hoover Aghababaie Tolley, CB, de Rham Hoover

• 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.

62
The Worries
Albrecht, CB, Ravndal, Skordis Tolley, CB,
Hoover Aghababaie Tolley, CB, de Rham Hoover

• 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)

63
Prognosis

• Theoretical worries
• Observational tests

64
Observational Consequences

• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics?
• And more!

SUSY broken at the TeV scale,
but not the MSSM!
65
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

66
Observational Consequences

• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics

• Can there be observable signals if Mg 10 TeV?
• Must hit new states before E Mg . Eg string
  and KK states have MKK lt Ms lt Mg

67
Observational Consequences

• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics

• Can there be observable signals if Mg 10 TeV?
• Must hit new states before E Mg . Eg string
  and KK states have MKK lt Ms lt Mg
• Dimensionless couplings to bulk scalars are
  unsuppressed by Mg

68
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
Detailed Worries and Observations

• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics?

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

70
Backup slides
71
The Worries

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

72
The Worries
Salam Sezgin

• 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
  ef r2 constant.
• Loops lift this flat direction, and in so doing
  give dynamics to f and r.

73
The Worries
Kantowski Milton Albrecht, CB, Ravndal, Skordis
CB Hoover Ghilencea, Hoover, CB Quevedo

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

Potential domination when
Canonical Variables
74
The Worries
Albrecht, CB, Ravndal, Skordis

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

Potential domination when
Hubble damping can allow potential domination
for exponentially large r, even though r is not
stabilized.
Canonical Variables
75
The Worries

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

76
The Worries
Nilles et al Cline et al Erlich et al

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

• Why isnt this killed by what killed 5D
  self-tuning?
• In 5D models, presence of one brane with
  nonzero positive tension T1 implied a singularity
  in the bulk.
• Singularity can be interpreted as presence of a
  second brane whose tension T2 need be negative.
  This is a hidden fine tuning
• T1 T2 0

77
The Worries
Nilles et al Cline et al Erlich et al

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

• Why isnt this killed by what killed 5D
  self-tuning?
• In 5D models, presence of one brane with
  nonzero positive tension T1 implied a singularity
  in the bulk.
• Singularity can be interpreted as presence of a
  second brane whose tension T2 need be negative.
  This is a hidden fine tuning
• T1 T2 0

78
The Worries
Nilles et al Cline et al Erlich et al

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

• Why isnt this killed by what killed 5D
  self-tuning?
• In 5D models, presence of one brane with
  nonzero positive tension T1 implied a singularity
  in the bulk.
• Singularity can be interpreted as presence of a
  second brane whose tension T2 need be negative.
  This is a hidden fine tuning
• T1 T2 0

• 6D analog corresponds to the Euler number
  topological constraint

79
The Worries
Nilles et al Cline et al Erlich et al

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

• Why isnt this killed by what killed 5D
  self-tuning?
• In 5D models, presence of one brane with
  nonzero positive tension T1 implied a singularity
  in the bulk.
• Singularity can be interpreted as presence of a
  second brane whose tension T2 need be negative.
  This is a hidden fine tuning
• T1 T2 0

• 6D analog corresponds to the Euler number
  topological constraint

• Being topological, this is preserved under
  renormalization. If S Tb nonzero then R becomes
  nonzero

80
The Worries

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

• Weinbergs 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
The Worries

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

• Weinbergs 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
The Worries

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

• Weinbergs 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
The Worries

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

• Nimas No-Go Argument
• One can have a vacuum energy m4 with m
  greater than the cutoff, provided it is turned on
  adiabatically.
• So having extra dimensions with r 1/m does
  not release one from having to find an
  intrinsically 4D mechanism.

84
The Worries

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

• Nimas No-Go Argument
• One can have a vacuum energy m4 with m
  greater than the cutoff, provided it is turned on
  adiabatically.
• So having extra dimensions with r 1/m does
  not release one from having to find an
  intrinsically 4D mechanism.

• Scale invariance precludes obtaining m greater
  than the cutoff in an adiabatic way

implies
85
The Worries

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

86
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 Newtons constant, its
  motion between BBN and now will cause
  unacceptably large changes to G.

87
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 Newtons 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
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 Newtons 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
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
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
The Worries

• Technical Naturalness
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars

92
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
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) c0 M4 c1 M2/r2 c2 /r4
• then c0 c1 0 ensures both small mass and
  small dark energy.

94
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
• Isnt such a light scalar already ruled out
  by precision tests of GR in the solar system?

95
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
• Isnt 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 f rolls. Can arrange these
to be small here now.
96
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
• Isnt 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 f rolls. Can arrange these
to be small here now.
a vs log a
97
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
• Shouldnt there be strong bounds due to
  energy losses from red giant stars and
  supernovae? (Really a bound on LEDs and not on
  scalars.)

98
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
• Shouldnt 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
Observational Consequences

• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics

100
Observational Consequences
Albrecht, CB, Ravndal Skordis Kainulainen
Sunhede

• 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

101
Observational Consequences
Albrecht, CB, Ravndal Skordis

• 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

Potential domination when
Canonical Variables
102
Observational Consequences
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

• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics

log r vs log a
103
Observational Consequences
Albrecht, CB, Ravndal Skordis

• L 0.7

• 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

• m 0.25

• and w
• vs log a

Radiation Matter Total Scalar w Parameter
w 0.9
104
Observational Consequences
Albrecht, CB, Ravndal Skordis

• 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

a vs log a
105
Observational Consequences
Albrecht, CB, Ravndal Skordis

• 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

log r vs log a
106
Observational Consequences

• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics

• At small distances
• Changes Newtons Law at range r/2p 1 mm.
• At large distances
• Scalar-tensor theory out to distances of order
  H0.

107
Observational Consequences

• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics

• At small distances
• Changes Newtons Law at range r/2p 1 mm.
• At large distances
• Scalar-tensor theory out to distances of order
  H0.

108
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

109
Observational Consequences

• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics

• Can there be observable signals if Mg 10 TeV?
• Must hit new states before E Mg . Eg string
  and KK states have MKK lt Ms lt Mg
• Dimensionless couplings to bulk scalars are
  unsuppressed by Mg

110
Observational Consequences
Azuelos, Beauchemin CB

• 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

Dimensionless coupling! O(0.1-0.001) from
loops
111
Observational Consequences
Azuelos, Beauchemin CB

• 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

Dimensionless coupling! O(0.1-0.001) from
loops

• Use H decay into gg, so search for two hard
  photons plus missing ET.

112
Observational Consequences
Azuelos, Beauchemin CB

• 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

• Standard Model backgrounds

113
Observational Consequences
Azuelos, Beauchemin CB

• 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

114
Observational Consequences
Azuelos, Beauchemin CB

• 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

• Significance of signal vs cut on missing ET

115
Observational Consequences
Azuelos, Beauchemin CB

• 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

• Possibility of missing-ET cut improves the reach
  of the search for Higgs through its gg channel

116
Observational Consequences
Matias, CB

• 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.

117
Observational Consequences
Matias, CB

• 6D supergravities have many bulk fermions
• Gravity (gmn, ym, Bmn, c, j)
• Gauge (Am, l)
• Hyper (F, x)
• 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

• 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

118
Observational Consequences
Matias, CB

• 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 l 1/Mg
119
Observational Consequences
Matias, CB

• 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

• SUSY keeps N massless in bulk
• Natural mixing with Goldstino on branes
• Chirality in extra dimensions provides natural L

Dimensionful coupling l 1/Mg
120
Observational Consequences
Matias, CB

• 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! l 1/Mg
121
Observational Consequences
Matias, CB
t
Constrained by bounds on sterile neutrino emission

• 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! l 1/Mg
Require observed masses and large mixing.
122
Observational Consequences
Matias, CB
t
Constrained by bounds on sterile neutrino emission

• 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

• Bounds on sterile neutrinos easiest to satisfy if
  g l v lt 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.

Dimensionful coupling! l 1/Mg
Require observed masses and large mixing.
123
Observational Consequences
Matias, CB

• Imagine lepton-breaking terms are suppressed.
• Possibly generated by loops in running to low
  energies from Mg.
• Acquire desired masses and mixings with a mild
  hierarchy for g/g and e/e.
• Build in approximate Le Lm Lt, and Z2
  symmetries.

• 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

S Mg r
124
Observational Consequences
Matias, CB

• 1 massless state
• 2 next- lightest states have strong overlap with
  brane.
• Inverted hierarchy.
• Massive KK states mix weakly.

• 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

125
Observational Consequences
Matias, CB
Worrisome once we choose g 10-4, good masses
for the light states require e S k
1/g Must get this from a real compactification.

• 1 massless state
• 2 next- lightest states have strong overlap with
  brane.
• Inverted hierarchy.
• Massive KK states mix weakly.

• 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

126
Observational Consequences
Matias, CB

• 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

2

• Lightest 3 states can have acceptable 3-flavour
  mixings.
• Active sterile mixings can satisfy incoherent
  bounds provided g 10-4 or less (qi g/ci).

127
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