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Extra Dimensions and the Cosmological Constant Problem

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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
  • Albrecht, F. Ravndal, C. Skordis

3
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

4
Naturalness as an Opportunity
  • 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.
  • Progress will come by combining both

5
The Cosmological Constant Problem
  • Dark energy vs vacuum energy
  • Why must the vacuum energy be large?

6
The Cosmological Constant Problem
Concordance cosmology points to several types of
cosmic matter
  • Dark energy vs vacuum energy
  • Why must the vacuum energy be large?

7
The Cosmological Constant Problem
N. Wright, astro-ph/0701584
  • Dark energy vs vacuum energy
  • Why must the vacuum energy be large?

w pDE/rDE -1 for a cosmological constant
8
The Cosmological Constant Problem
  • Hierarchy Problems
  • Why Extra Dimensions?

A cosmological constant is not distinguishable
from a Lorentz invariant vacuum energy vs
9
The Cosmological Constant Problem
  • Hierarchy Problems
  • Why Extra Dimensions?

A cosmological constant is not distinguishable
from a Lorentz invariant vacuum energy vs
in 4 dimensions
10
The Cosmological Constant Problem
  • Dark energy vs vacuum energy
  • Why must the vacuum energy be large?

11
The Cosmological Constant Problem
  • Dark energy vs vacuum energy
  • Why must the vacuum energy be large?

The observed dark energy density corresponds to
a very small vacuum energy implies
12
The Cosmological Constant Problem
  • Dark energy vs vacuum energy
  • Why must the vacuum energy be large?

BUT particles of mass m contribute m m
13
The Cosmological Constant Problem
  • Dark energy vs vacuum energy
  • Why must the vacuum energy be large?

BUT particles of mass m contribute m m
14
The Cosmological Constant Problem
  • Dark energy vs vacuum energy
  • Why must the vacuum energy be large?

BUT particles of mass m contribute m m
15
The Cosmological Constant Problem
  • Dark energy vs vacuum energy
  • Why must the vacuum energy be large?

BUT particles of mass m contribute m m
Must cancel to 32 decimal places!!
16
The Cosmological Constant Problem
  • Dark energy vs vacuum energy
  • Why must the vacuum energy be large?

BUT particles of mass m contribute m m
17
The Cosmological Constant Problem
  • Dark energy vs vacuum energy
  • Why must the vacuum energy be large?

BUT particles of mass m contribute m m
Must cancel to 40 decimal places!!
18
Technical Naturalness
  • Given a small quantity r r0 dr
  • In the fundamental theory, why should r0 be
    small?
  • Given that r0 is small, why does it stay small as
    one integrates out physics up to the scales for
    which r is measured?

19
Technical Naturalness
  • This may have to wait until we know the
    fundamental theory.
  • Given a small quantity r r0 dr
  • In the fundamental theory, why should r0 be
    small?
  • Given that r0 is small, why does it stay small as
    one integrates out physics up to the scales for
    which r is measured?

20
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 r r0 dr
  • In the fundamental theory, why should r0 be
    small?
  • Given that r0 is small, why does it stay small as
    one integrates out physics up to the scales for
    which r is measured?

21
The Cosmological Constant Problem
  • 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?
22
Another Naturalness Problem
  • Dark energy vs vacuum energy
  • Why must the vacuum energy be large?

r is a constant if it is vacuum energy
23
Another Naturalness Problem
  • Dark energy vs vacuum energy
  • Why must the vacuum energy be large?

More complicated time-dependence is possible
24
Another Naturalness Problem
  • Dark energy vs vacuum energy
  • Why must the vacuum energy be large?

When time dependence is due to scalar field
motion, the scalar field mass must be very small
BUT contributions to mf are of order
so are too large if M gt 10-2 eV
25
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

26
How Extra Dimensions Help
  • 4D CC vs 4D vacuum energy
  • Branes and scales

27
How Extra Dimensions Help
New Tools motivated by string theory (or
condensed matter) Particles can be localized
on surfaces (branes, or defects) within the extra
dimensions Gravity is not similarly localized
  • 4D CC vs 4D vacuum energy
  • Branes and scales

28
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

Arkani-Hamad et al Kachru et al, Carroll
Guica Aghababaie, et al
29
How Extra Dimensions Help
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

30
How Extra Dimensions Help
To be useful it must be that extra dimensions
can be as large as the observed Dark Energy
density c/r 10-2 eV or r 1
m-metre This is possible! provided all known
particles except gravity are trapped on a brane,
since tests of Newtons law allow r lt 50
m-metre
  • 4D CC vs 4D vacuum energy
  • Branes and scales

Arkani Hamed, Dvali, Dimopoulos
Adelberger et al
31
How Extra Dimensions Help
Arkani Hamed, Dvali, Dimopoulos
If there are extra dimensions as large as r 1
m-metre then there can only be two of them
(although others could exist if they are much
smaller), or else the observed strength of
gravity would require the scale of
extra-dimensional physics to be smaller than
mw with n extra dimensions
  • 4D CC vs 4D vacuum energy
  • Branes and scales

32
How Extra Dimensions Help
  • 4D CC vs 4D vacuum energy
  • Branes and scales

These scales are natural using standard 4D
arguments.
33
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!
34
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

35
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.

36
The SLED Proposal
  • Suppose physics is extra-dimensional above the
    10-2 eV scale.
  • Suppose the physics of the bulk is supersymmetric.
  • Bulk supersymmetry
  • SUSY breaks at scale Mg on the branes
  • Trickle-down of SUSY breaking to the bulk is

37
The SLED Proposal
Particle Spectrum
SM on brane no partners Many KK modes
in bulk
4D scalar ef r2 const
4D graviton
38
The CC Problem in 6D
  • The 6D CC
  • Integrate out brane physics
  • Integrate out bulk physics
  • Classical contribution
  • Quantum corrections

39
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.

40
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.

41
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)

42
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

43
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

44
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!!
45
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!!
46
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.

47
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

48
Prognosis
  • Theoretical worries
  • Observational tests

49
The Worries
  • Technical Naturalness
  • Runaway Behaviour
  • Stabilizing the Extra Dimensions
  • Famous No-Go Arguments
  • Problems with Cosmology
  • Constraints on Light Scalars

50
The Worries
  • Technical Naturalness
  • Runaway Behaviour
  • Stabilizing the Extra Dimensions
  • Famous No-Go Arguments
  • Problems with Cosmology
  • Constraints on Light Scalars

51
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?

52
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)

53
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

54
The Worries
  • Technical Naturalness
  • Runaway Behaviour
  • Stabilizing the Extra Dimensions
  • Famous No-Go Arguments
  • Problems with Cosmology
  • Constraints on Light Scalars

55
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.

56
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)

57
Prognosis
  • Theoretical worries
  • Observational tests

58
The Observational Tests
  • Quintessence cosmology

59
The Observational Tests
  • Quintessence cosmology
  • Modifications to gravity

60
The Observational Tests
  • Quintessence cosmology
  • Modifications to gravity
  • Collider physics

61
The Observational Tests
  • Quintessence cosmology
  • Modifications to gravity
  • Collider physics

SUSY broken at the TeV scale,
but not the MSSM!
62
The Observational Tests
  • Quintessence cosmology
  • Modifications to gravity
  • Collider physics
  • Neutrino physics?

63
The Observational Tests
  • Quintessence cosmology
  • Modifications to gravity
  • Collider physics
  • Neutrino physics?
  • And more!

64
Summary
  • 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.

65
Summary
  • 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?

66
Summary
  • 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.

67
Summary
  • 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

68
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

69
Backup slides
70
The Worries
  • Technical Naturalness
  • Runaway Behaviour
  • Stabilizing the Extra Dimensions
  • Famous No-Go Arguments
  • Problems with Cosmology
  • Constraints on Light Scalars

71
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.

72
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
73
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
74
The Worries
  • Technical Naturalness
  • Runaway Behaviour
  • Stabilizing the Extra Dimensions
  • Famous No-Go Arguments
  • Problems with Cosmology
  • Constraints on Light Scalars

75
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

76
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

77
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

78
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.

79
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 \mu greater
    than the cutoff in an adiabatic way

implies
80
The Worries
  • Technical Naturalness
  • Runaway Behaviour
  • Stabilizing the Extra Dimensions
  • Famous No-Go Arguments
  • Problems with Cosmology
  • Constraints on Light Scalars

81
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.

82
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.

83
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
84
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

85
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

86
The Worries
  • Technical Naturalness
  • Runaway Behaviour
  • Stabilizing the Extra Dimensions
  • Famous No-Go Arguments
  • Problems with Cosmology
  • Constraints on Light Scalars

87
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?

88
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.

89
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?

90
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.
91
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
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
  • Shouldnt there be strong bounds due to
    energy losses from red giant stars and
    supernovae? (Really a bound on LEDs and not on
    scalars.)

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
  • 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.

94
Observational Consequences
  • Quintessence cosmology
  • Modifications to gravity
  • Collider physics
  • Neutrino physics
  • Astrophysics

95
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

96
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
97
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
98
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
99
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
100
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
101
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.

102
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.

103
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

104
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

105
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
106
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.

107
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

108
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

109
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

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

111
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.

112
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

113
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
114
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
115
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
116
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.
117
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.
118
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
119
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

120
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

121
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).

122
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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