The Cosmological Constant on the Brane

1
The Cosmological Constant on the Brane

• New Approaches
• to Naturalness
• Cliff Burgess

2
Partners in Crime

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

3
The Plan

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

4
Naturalness and Dark Energy

• Why doesnt the electron contribute too large a
  zero-point energy to the cosmological constant?

5
Technical Naturalness

• This may have to wait until we know the
  fundamental theory.
• This is serious because it involves physics we
  think we understand

• Given a small quantity l l0 dl
• In the fundamental theory, why should l0 be
  small?
• Given that l0 is small, why does it stay small as
  one integrates out physics up to the scales for
  which l is measured?

6
Anthropism v. Technical Naturalness

• Given a small quantity l l0 dl
• Why cant l0 cancel dl?
• 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

• 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.

• Given a small quantity l l0 dl
• Why cant l0 cancel dl?
• Given enough vacua perhaps this cancellation
  occurs in some.
• It may only be possible to discuss this problem
  in those vacua where cancellation occurs.

8
Scales
How can these scales be changed to reduce the
vacuum energys gravity?
These scales are natural using standard 4D
arguments.
9
Vacuum Energy 4D Curvature
Arkani-Hamad et al Kachru et al, Carroll
Guica Aghababaie, et al

• In 4D a Lorentz-invariant vacuum energy
  necessarily gravitates like a cosmological
  constant.
• In higher dimensions a 4D vacuum energy on a
  brane can curve the extra dimensions instead of
  the observed 4 dimensions.

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 Mg on the branes
• Trickle-down of SUSY breaking to the bulk is

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

• 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.

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
Chen, Luty Ponton

• 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!!
21
The CC Problem in 6D
Aghababaie et al.

• 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!!
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 msb 10-2
  eV
• Quantum corrections can be right size in absence
  of msb2 Mg2 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
What Needs Understanding

• Classical part of the argument
• What choices must be made to ensure 4D flatness?
• Quantum part of the argument
• Are these choices stable against renormalization?

• Search for solutions to 6D supergravity
• What bulk geometry arises from a given brane
  configuration?

25
What Needs Understanding

• Classical part of the argument
• What choices must be made to ensure 4D flatness?
• Quantum part of the argument
• Are these choices stable against renormalization?

• Search for solutions to 6D supergravity
• What kind of bulk geometry arises from a given
  pair of branes?

26
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

27
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

28
6D Solutions No Branes

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

29
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!

30
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

31
6D Solutions Conical Singularities
Gibbons, Guven Pope Aghababaie, CB, Cline,
Firouzjahi, Parameswaran, Quevedo Tasinato
Zavala

• General solutions with two conical
  singularities
• Unequal conical defects lead to warped
  geometries in the bulk
• All such (static) solutions have flat 4D
  geometries

32
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

33
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

34
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

35
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

36
6D Solutions Time-dependence
Tolley, CB, de Rham Hoover

• 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

37
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.

38
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 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 Weinbergs Theorem?

• Weinberg has a general objection to self-tuning
  mechanisms for solving the cosmological constant
  problem.

40
What About Weinbergs Theorem?

• Weinberg has a general objection to self-tuning
  mechanisms for solving the cosmological constant
  problem.

41
What About Weinbergs Theorem?

• Weinberg has a general objection to self-tuning
  mechanisms for solving the cosmological constant
  problem.

42
What About Weinbergs 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
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

45
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
46
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
47
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
48
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
49
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
50
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.

51
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.

52
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

53
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
54
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
55
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

56
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

57
Observational Consequences
Matias, CB London

• 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.

58
Observational Consequences
Matias, CB London

• 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

59
Observational Consequences
Matias, CB London

• 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
60
Observational Consequences
Matias, CB London

• 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
61
Observational Consequences
Matias, CB London

• 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
62
Observational Consequences
Matias, CB London
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.
63
Observational Consequences
Matias, CB London
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 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.
64
Observational Consequences
Matias, CB London

• 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
65
Observational Consequences
Matias, CB London

• 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

66
Observational Consequences
Matias, CB London
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

67
Observational Consequences
Matias, CB London

• 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).

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?