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Extra Dimensions and the Cosmological Constant Problem

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Extra dimensions could start here, if there are only two of them. ... Suppose physics is extra-dimensional above the 10-2 eV scale. ... – PowerPoint PPT presentation

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Title: 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
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