extra dimensions and the cosmological constant problem
DESCRIPTION
Extra Dimensions and the Cosmological Constant Problem. Cliff Burgess. 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: - PowerPoint PPT PresentationTRANSCRIPT
Dark Energy 2007
Extra Dimensions and the Cosmological Constant Problem
Cliff Burgess
Dark Energy 2007
Partners in Crime
• CC Problem:• Y. Aghababaie, J. Cline, C. de Rham, H. Firouzjahi,
D. Hoover, S. Parameswaran, F. Quevedo, G. Tasinato, A. Tolley, I. Zavala
• Phenomenology:• G. Azuelos, P.-H. Beauchemin, J. Matias, F. Quevedo
• Cosmology:• Albrecht, F. Ravndal, C. Skordis
Dark Energy 2007
The Plan
• The Cosmological Constant problem• Why is it so hard?
• How extra dimensions might help• Changing how the vacuum energy gravitates
• Making things concrete• 6 dimensions and supersymmetry
• Prognosis• Technical worries
• Observational tests
Dark Energy 2007
‘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
Dark Energy 2007
The Cosmological Constant Problem
• Dark energy vs vacuum energy
• Why must the vacuum energy be large?
Dark Energy 2007
The Cosmological Constant Problem
• Dark energy vs vacuum energy
• Why must the vacuum energy be large?
Concordance cosmology points to several types of cosmic ‘matter’:
mDMDE TTTGG 8
mni
ii
gpT
0
0
0 mDM pp
Dark Energy 2007
The Cosmological Constant Problem
• Dark energy vs vacuum energy
• Why must the vacuum energy be large?
w = pDE/D for a cosmological constant
N. Wright, astro-ph/0701584
Dark Energy 2007
The Cosmological Constant Problem
• Hierarchy Problems
• Why Extra Dimensions?
A cosmological constant is not distinguishable from a Lorentz invariant vacuum energy
vs
gGTGG 488
TGgG 8
Dark Energy 2007
The Cosmological Constant Problem
• Hierarchy Problems
• Why Extra Dimensions?
A cosmological constant is not distinguishable* from a Lorentz invariant vacuum energy
vs
gGTGG 488
TGgG 8
* in 4 dimensions…
Dark Energy 2007
The Cosmological Constant Problem
• Dark energy vs vacuum energy
• Why must the vacuum energy be large?
Dark Energy 2007
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
329534 cm/g10/ c
V10 2 e
Dark Energy 2007
The Cosmological Constant Problem
• Dark energy vs vacuum energy
• Why must the vacuum energy be large?
42 V10 e
me ~ 106 eV
m10-2 eV
mw ~1011 eV
m ~ 108 eV
BUT: particles of mass m contribute » m:
Dark Energy 2007
The Cosmological Constant Problem
• Dark energy vs vacuum energy
• Why must the vacuum energy be large?
42 V10 e
me ~ 106 eV
m10-2 eV
mw ~1011 eV
m ~ 108 eV
40 mk
BUT: particles of mass m contribute » m:
Dark Energy 2007
The Cosmological Constant Problem
• Dark energy vs vacuum energy
• Why must the vacuum energy be large?
42 V10 e
me ~ 106 eV
m10-2 eV
mw ~1011 eV
m ~ 108 eV
40 mk
441 mkmk ee
BUT: particles of mass m contribute » m:
Dark Energy 2007
The Cosmological Constant Problem
• Dark energy vs vacuum energy
• Why must the vacuum energy be large?
42 V10 e
me ~ 106 eV
m10-2 eV
mw ~1011 eV
m ~ 108 eV
40 mk
441 mkmk ee
BUT: particles of mass m contribute » m:
Must cancel to 32 decimal places!!
Dark Energy 2007
The Cosmological Constant Problem
• Dark energy vs vacuum energy
• Why must the vacuum energy be large?
42 V10 e
me ~ 106 eV
m10-2 eV
mw ~1011 eV
m ~ 108 eV
441 mkmk ee
BUT: particles of mass m contribute » m:
...442 ee mkmk
40 mk
Dark Energy 2007
The Cosmological Constant Problem
• Dark energy vs vacuum energy
• Why must the vacuum energy be large?
42 V10 e
me ~ 106 eV
m10-2 eV
mw ~1011 eV
m ~ 108 eV
441 mkmk ee
BUT: particles of mass m contribute » m:
...442 ee mkmk
40 mk
Must cancel to 40 decimal places!!
Dark Energy 2007
The Cosmological Constant Problem
• Dark energy vs vacuum energy
• Why must the vacuum energy be large?
me ~ 106 eV
m10-2 eV
mw ~1011 eV
m ~ 108 eV
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?
Dark Energy 2007
Another Naturalness Problem
• Dark energy vs vacuum energy
• Why must the vacuum energy be large?
is a constant if it is vacuum energy
Dark Energy 2007
Another Naturalness Problem
• Dark energy vs vacuum energy
• Why must the vacuum energy be large?
More complicated time-dependence is possible
Dark Energy 2007
Another Naturalness Problem
• Dark energy vs vacuum energy
• Why must the vacuum energy be large?
BUT: contributions to m are of order
so are too large if M > 10-2 eV
When time dependence is due to scalar field motion, the scalar field mass must be very small:
eVMHm p332 10/
pMMgMm /2
Dark Energy 2007
The Plan
• The Cosmological Constant problem• Why is it so hard?
• How extra dimensions might help• Changing how the vacuum energy gravitates
• Making things concrete• 6 dimensions and supersymmetry
• Prognosis• Technical worries
• Observational tests
Dark Energy 2007
How Extra Dimensions Help
• 4D CC vs 4D vacuum energy
• Branes and scales
Dark Energy 2007
How Extra Dimensions Help
• 4D CC vs 4D vacuum energy
• Branes and scales
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
Dark Energy 2007
How Extra Dimensions Help
• 4D CC vs 4D vacuum energy
• Branes and scales
In higher dimensions a 4D vacuum energy, if localized in the extra dimensions, can curve the extra dimensions instead of the observed four.
Arkani-Hamad et alKachru et al,
Carroll & GuicaAghababaie, et al
Dark Energy 2007
How Extra Dimensions Help
• 4D CC vs 4D vacuum energy
• Branes and scales• Most general 4D flat solutions to chiral 6D
supergravity, without matter fields.
• 3 nonzero gives curvature singularities at branes
Gibbons, Guven & Pope
Dark Energy 2007
How Extra Dimensions Help
• 4D CC vs 4D vacuum energy
• Branes and scales
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 -metre
This is possible! provided all known particles except gravity are trapped on a brane, since tests of Newton’s law allow
r < 50 -metre Adelberger et al
Arkani Hamed, Dvali, Dimopoulos
Dark Energy 2007
How Extra Dimensions Help
• 4D CC vs 4D vacuum energy
• Branes and scales
If there are extra dimensions as large as r » 1 -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
2/nggp rMMM
Arkani Hamed, Dvali, Dimopoulos
Dark Energy 2007
How Extra Dimensions Help
• 4D CC vs 4D vacuum energy
• Branes and scales These scales are natural using standard 4D arguments.
m ~ mw2/Mp
~ 10-2 eV
H ~ m2/Mp
mw
Dark Energy 2007
How Extra Dimensions Help
• 4D CC vs 4D vacuum energy
• Branes and scales
Only gravity gets modified over the most dangerous distance scales!
m ~ mw2/Mp
~ 10-2 eV
H ~ m2/Mp
mw Must rethink how the vacuum gravitates in 6D for these scales.
SM interactions do not change at all!
Dark Energy 2007
The Plan
• The Cosmological Constant problem• Why is it so hard?
• How extra dimensions might help• Changing how the vacuum energy gravitates
• Making things concrete• 6 dimensions and supersymmetry
• Prognosis• Technical worries
• Observational tests
Dark Energy 2007
The SLED Proposal
• Suppose physics is extra-dimensional above the 10-2 eV scale.
• Suppose the physics of the bulk is supersymmetric.
Aghababaie, CB, Parameswaran & Quevedo
Dark Energy 2007
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:
eV101 2
2
rM
Mm
p
gSB
Dark Energy 2007
The CC Problem in 6D
• The 6D CC
• Integrate out brane physics
• Integrate out bulk physics• Classical contribution• Quantum corrections
Dark Energy 2007
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.
Dark Energy 2007
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.
Nishino & Sezgin
Dark Energy 2007
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)
ii
i yyT 2
Dark Energy 2007
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
smoothii
i RyyTR 2
Dark Energy 2007
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
...2 RgydTi
ieff
smoothii
i RyyTR 2
Dark Energy 2007
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
...2 RgydTi
ieff
smoothii
i RyyTR 2
Tensions cancel between brane and bulk!!
Chen, Luty & Ponton
Dark Energy 2007
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
...2 RgydTi
ieff
smoothii
i RyyTR 2
Smooth parts also cancel for supersymmetric theories!!
Aghababaie et al.
Dark Energy 2007
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 msb
2 Mg2 terms!
• Lifts flat direction.
4sbm
Dark Energy 2007
The Plan
• The Cosmological Constant problem• Why is it so hard?
• How extra dimensions might help• Changing how the vacuum energy gravitates
• Making things concrete• 6 dimensions and supersymmetry
• Prognosis• Technical worries• Observational tests
Dark Energy 2007
Prognosis
• Theoretical worries
• Observational tests
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• Classical part of the argument:• What choices must be made to ensure 4D
flatness?
• Quantum part of the argument:• Are these choices stable against
renormalization?
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• Classical part of the argument:• What choices must be made to ensure 4D
flatness?
Now understand how 2 extra dimensions respond to presence of 2 branes having arbitrary couplings.• Not all are flat in 4D, but all of those
having only conical singularities are flat. (Conical singularities correspond to
absence of dilaton couplings to branes)
Tolley, CB, Hoover & Aghababaie
Tolley, CB, de Rham & HooverCB, Hoover & Tasinato
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• Quantum part of the argument:• Are these choices stable against
renormalization?
So far so good, but not yet complete• Brane loops cannot generate dilaton
couplings if these are not initially present• Bulk loops can generate such couplings,
but are suppressed by 6D supersymmetry
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• Most brane properties and initial conditions do not lead to anything like the universe we see around us.• For many choices the extra dimensions
implode or expand to infinite size.
Albrecht, CB, Ravndal, Skordis Tolley, CB, Hoover & Aghababaie
Tolley, CB, de Rham & Hoover
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• Most brane properties and initial conditions do not lead to anything like the universe we see around us.• For many choices the extra dimensions
implode or expand to infinite size.
• Initial condition problem: much like the Hot Big Bang, possibly understood by reference to earlier epochs of cosmology (eg: inflation)
Albrecht, CB, Ravndal, Skordis Tolley, CB, Hoover & Aghababaie
Tolley, CB, de Rham & Hoover
Dark Energy 2007
Prognosis
• Theoretical worries
• Observational tests
Dark Energy 2007
The Observational Tests
• Quintessence cosmology
Dark Energy 2007
The Observational Tests
• Quintessence cosmology
• Modifications to gravity
Dark Energy 2007
The Observational Tests
• Quintessence cosmology
• Modifications to gravity
• Collider physics
Dark Energy 2007
The Observational Tests
• Quintessence cosmology
• Modifications to gravity
• Collider physics SUSY broken at the TeV scale,
but not the MSSM!
Dark Energy 2007
The Observational Tests
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics?
Dark Energy 2007
The Observational Tests
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics?
• And more!
Dark Energy 2007
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.
Dark Energy 2007
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?
Dark Energy 2007
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.
Dark Energy 2007
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…
Dark Energy 2007
Detailed Worries and Observations
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics?
Dark Energy 2007
Backup slides
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• Classical flat direction corresponding to combination of radius and dilaton: e r2 = constant.
• Loops lift this flat direction, and in so doing give dynamics to and r.
Salam & Sezgin
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars ]exp[)( 2 cbaV
42 1
)](log)log([r
rMcrMbaV
2
22
r
rML pkin
)/exp(0' baMrifV
Potential domination when:
Canonical Variables:
Kantowski & MiltonAlbrecht, CB, Ravndal, Skordis
CB & HooverGhilencea, Hoover, CB &
Quevedo
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars ]exp[)( 2 cbaV
42 1
)](log)log([r
rMcrMbaV
2
22
r
rML pkin
)/exp(0' baMrifV
Potential domination when:
Canonical Variables:
Albrecht, CB, Ravndal, Skordis
Hubble damping can allow potential domination for exponentially large r, even though r is not stabilized.
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• Weinberg’s No-Go Theorem:
Steven Weinberg has a general objection to self-tuning mechanisms for solving the cosmological constant problem that are based on scale invariance
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• Weinberg’s No-Go Theorem:
Steven Weinberg has a general objection to self-tuning mechanisms for solving the cosmological constant problem that are based on scale invariance
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• Weinberg’s No-Go Theorem:
Steven Weinberg has a general objection to self-tuning mechanisms for solving the cosmological constant problem that are based on scale invariance
4
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• Nima’s No-Go Argument:
One can have a vacuum energy 4 with greater than the cutoff, provided it is turned on adiabatically.
So having extra dimensions with r ~ 1/ does not release one from having to find an intrinsically 4D mechanism.
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• Nima’s No-Go Argument:
One can have a vacuum energy 4 with greater than the cutoff, provided it is turned on adiabatically.
So having extra dimensions with r ~ 1/ does not release one from having to find an intrinsically 4D mechanism.
• Scale invariance precludes obtaining \mu greater than the cutoff in an adiabatic way:
eVeff4 implies 42
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• Post BBN:
Since r controls Newton’s constant, its motion between BBN and now will cause unacceptably large changes to G.
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• Post BBN:
Since r controls Newton’s constant, its motion between BBN and now will cause unacceptably large changes to G.
Even if the kinetic energy associated with r were to be as large as possible at BBN, Hubble damping keeps it from rolling dangerously far between then and now.
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• Post BBN:
Since r controls Newton’s constant, its motion between BBN and now will cause unacceptably large changes to G.
Even if the kinetic energy associated with r were to be as large as possible at BBN, Hubble damping keeps it from rolling dangerously far between then and now.
log r vs log a
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• Pre BBN:
There are strong bounds on KK modes in models with large extra dimensions from:
* their later decays into photons; * their over-closing the Universe; * their light decay products being too
abundant at BBN
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• Pre BBN:
There are strong bounds on KK modes in models with large extra dimensions from:
* their later decays into photons; * their over-closing the Universe; * their light decay products being too
abundant at BBN
Photon bounds can be evaded by having invisible channels; others are model dependent, but eventually must be addressed
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• A light scalar with mass m ~ H has several generic difficulties:
What protects such a small mass from large quantum corrections?
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• A light scalar with mass m ~ H has several generic difficulties:
What protects such a small mass from large quantum corrections?
Given a potential of the form
V(r) = c0 M4 + c1 M2/r2 + c2 /r4 + …
then c0 = c1 = 0 ensures both small mass and small dark energy.
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• A light scalar with mass m ~ H has several generic difficulties:
Isn’t such a light scalar already ruled out by precision tests of GR in the solar system?
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• A light scalar with mass m ~ H has several generic difficulties:
Isn’t such a light scalar already ruled out by precision tests of GR in the solar system?
The same logarithmic corrections which enter the potential can also appear in its matter couplings, making them field dependent and so also time-dependent as rolls.
Can arrange these to be small here & now.
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• A light scalar with mass m ~ H has several generic difficulties:
Isn’t such a light scalar already ruled out by precision tests of GR in the solar system?
The same logarithmic corrections which enter the potential can also appear in its matter couplings, making them field dependent and so also time-dependent as rolls.
Can arrange these to be small here & now. vs log a
03.0
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• A light scalar with mass m ~ H has several generic difficulties:
Shouldn’t there be strong bounds due to energy losses from red giant stars and supernovae? (Really a bound on LEDs and not on scalars.)
Dark Energy 2007
The Worries
• ‘Technical Naturalness’
• Runaway Behaviour
• Stabilizing the Extra Dimensions
• Famous No-Go Arguments
• Problems with Cosmology
• Constraints on Light Scalars
• A light scalar with mass m ~ H has several generic difficulties:
Shouldn’t there be strong bounds due to energy losses from red giant stars and supernovae? (Really a bound on LEDs and not on scalars.)
Yes, and this is how the scale M ~ 10 TeV for gravity in the extra dimensions is obtained.
Dark Energy 2007
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
Dark Energy 2007
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
• Quantum vacuum energy lifts flat direction.
• Specific types of scalar interactions are predicted.• Includes the Albrecht-
Skordis type of potential
• Preliminary studies indicate it is possible to have viable cosmology:• Changing G; BBN;…
Albrecht, CB, Ravndal & SkordisKainulainen & Sunhede
Dark Energy 2007
• Quantum vacuum energy lifts flat direction.
• Specific types of scalar interactions are predicted.• Includes the Albrecht-
Skordis type of potential
• Preliminary studies indicate it is possible to have viable cosmology:• Changing G; BBN;…
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
Albrecht, CB, Ravndal & Skordis
]exp[)( 2 cbaV
42 1
)](log)log([r
rMcrMbaV
2
22
r
rML pkin
)/exp(0' baMrifV
Potential domination when:
Canonical Variables:
Dark Energy 2007
• Quantum vacuum energy lifts flat direction.
• Specific types of scalar interactions are predicted.• Includes the Albrecht-
Skordis type of potential
• Preliminary studies indicate it is possible to have viable cosmology:• Changing G; BBN;…
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
Albrecht, CB, Ravndal & Skordis
log vs log a
Radiation
Matter
Total Scalar
Dark Energy 2007
• Quantum vacuum energy lifts flat direction.
• Specific types of scalar interactions are predicted.• Includes the Albrecht-
Skordis type of potential
• Preliminary studies indicate it is possible to have viable cosmology:• Changing G; BBN;…
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
Albrecht, CB, Ravndal & Skordis
Radiation
Matter
Total Scalar
w Parameter:
andw vs log a
~ 0.7
w ~ – 0.9
m ~ 0.25
Dark Energy 2007
• Quantum vacuum energy lifts flat direction.
• Specific types of scalar interactions are predicted.• Includes the Albrecht-
Skordis type of potential
• Preliminary studies indicate it is possible to have viable cosmology:• Changing G; BBN;…
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
Albrecht, CB, Ravndal & Skordis
vs log a
03.0
Dark Energy 2007
• Quantum vacuum energy lifts flat direction.
• Specific types of scalar interactions are predicted.• Includes the Albrecht-
Skordis type of potential
• Preliminary studies indicate it is possible to have viable cosmology:• Changing G; BBN;…
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
Albrecht, CB, Ravndal & Skordis
log r vs log a
Dark Energy 2007
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
• At small distances:• Changes Newton’s Law
at range r/2 ~ 1 m.
• At large distances• Scalar-tensor theory out
to distances of order H0.
Dark Energy 2007
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
• At small distances:• Changes Newton’s Law
at range r/2 ~ 1 m.
• At large distances• Scalar-tensor theory out
to distances of order H0.
Dark Energy 2007
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
Dark Energy 2007
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 < Ms < Mg
• Dimensionless couplings to bulk scalars are unsuppressed by Mg
Ms
MKK
Mg
Dark Energy 2007
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
byxHHxdaS ,*4
Dimensionless coupling! O(0.1-0.001) from loops
Azuelos, Beauchemin & CB
Dark Energy 2007
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
byxHHxdaS ,*4
Dimensionless coupling! O(0.1-0.001) from loops
Azuelos, Beauchemin & CB
• Use H decay into , so search for two hard photons plus missing ET.
Dark Energy 2007
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
Azuelos, Beauchemin & CB
• Standard Model backgrounds
Dark Energy 2007
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
Azuelos, Beauchemin & CB
Dark Energy 2007
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
Azuelos, Beauchemin & CB
• Significance of signal vs cut on missing ET
Dark Energy 2007
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
Azuelos, Beauchemin & CB
• Possibility of missing-ET cut improves the reach of the search for Higgs through its channel
Dark Energy 2007
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
• SLED predicts there are 6D massless fermions in the bulk, as well as their properties• Massless, chiral, etc.
• Masses and mixings can be chosen to agree with oscillation data.• Most difficult: bounds on
resonant SN oscillilations.
Matias, CB
Dark Energy 2007
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
• SLED predicts there are 6D massless fermions in the bulk, as well as their properties• Massless, chiral, etc.
• Masses and mixings can be naturally achieved which agree with data! • Sterile bounds;
oscillation experiments;
• 6D supergravities have many bulk fermions:• Gravity: (gmn, m, Bmn, , )• Gauge: (Am, )• Hyper: (, )
• Bulk couplings dictated by supersymmetry• In particular: 6D fermion masses must vanish
• Back-reaction removes KK zero modes• eg: boundary condition due to conical defect at
brane position
Matias, CB
Dark Energy 2007
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
• SLED predicts there are 6D massless fermions in the bulk, as well as their properties• Massless, chiral, etc.
• Masses and mixings can be naturally achieved which agree with data! • Sterile bounds;
oscillation experiments;
bauiiau yxNHLxdS ,4
Dimensionful coupling ~ 1/Mg
Matias, CB
Dark Energy 2007
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
• SLED predicts there are 6D massless fermions in the bulk, as well as their properties• Massless, chiral, etc.
• Masses and mixings can be naturally achieved which agree with data! • Sterile bounds;
oscillation experiments;
bauiiau yxNHLxdS ,4
Dimensionful coupling ~ 1/Mg
SUSY keeps N massless in bulk;
Natural mixing with Goldstino on branes;
Chirality in extra dimensions provides natural L;
Matias, CB
Dark Energy 2007
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
• SLED predicts there are 6D massless fermions in the bulk, as well as their properties• Massless, chiral, etc.
• Masses and mixings can be naturally achieved which agree with data! • Sterile bounds;
oscillation experiments;
bauiiau yxNHLxdS ,4
Dimensionful coupling! ~ 1/Mg
02
200
0
0
0
0
0
0
0
0
1
1
1
c
cvv
vv
vv
vvv
vvvrM
ee
e
e
Matias, CB
Dark Energy 2007
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
• SLED predicts there are 6D massless fermions in the bulk, as well as their properties• Massless, chiral, etc.
• Masses and mixings can be naturally achieved which agree with data! • Sterile bounds;
oscillation experiments;
t
bauiiau yxNHLxdS ,4
Dimensionful coupling! ~ 1/Mg
02
200
0
0
0
0
0
0
0
0
1
1
1
c
cvv
vv
vv
vvv
vvvrM
ee
e
e
Constrained by boundson sterile neutrino emission
Require observed masses and large mixing.
Matias, CB
Dark Energy 2007
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
• SLED predicts there are 6D massless fermions in the bulk, as well as their properties• Massless, chiral, etc.
• Masses and mixings can be naturally achieved which agree with data! • Sterile bounds;
oscillation experiments;
t
bauiiau yxNHLxdS ,4
Dimensionful coupling! ~ 1/Mg
02
200
0
0
0
0
0
0
0
0
1
1
1
c
cvv
vv
vv
vvv
vvvrM
ee
e
e
Constrained by boundson sterile neutrino emission
Require observed masses and large mixing.
• Bounds on sterile neutrinos easiest to satisfy if g = v < 10-4.
• Degenerate perturbation theory implies massless states strongly mix even if g is small.• This is a problem if there are massless KK
modes.• This is good for 3 observed flavours.
• Brane back-reaction can remove the KK zero mode for fermions.
Matias, CB
Dark Energy 2007
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
• SLED predicts there are 6D massless fermions in the bulk, as well as their properties• Massless, chiral, etc.
• Masses and mixings can be naturally achieved which agree with data! • Sterile bounds;
oscillation experiments;
• Imagine lepton-breaking terms are suppressed.• Possibly generated by
loops in running to low energies from Mg.
• Acquire desired masses and mixings with a mild hierarchy for g’/g and ’/• Build in approximate
Le – L – L, and Z2 symmetries.
g
g
g
g
')(
'
')(
g
1', SkM
km
M
m
g
KKKK
%102
''
g
g
S ~ Mg r
Matias, CB
Dark Energy 2007
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
• SLED predicts there are 6D massless fermions in the bulk, as well as their properties• Massless, chiral, etc.
• Masses and mixings can be naturally achieved which agree with data! • Sterile bounds;
oscillation experiments;
• 1 massless state• 2 next- lightest states
have strong overlap with brane.• Inverted hierarchy.
• Massive KK states mix weakly.
Matias, CB
Dark Energy 2007
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
• SLED predicts there are 6D massless fermions in the bulk, as well as their properties• Massless, chiral, etc.
• Masses and mixings can be naturally achieved which agree with data! • Sterile bounds;
oscillation experiments;
• 1 massless state• 2 next- lightest states
have strong overlap with brane.• Inverted hierarchy.
• Massive KK states mix weakly.
Worrisome: once we choose g ~ 10-4, good masses for the light states require: S = k ~ 1/g
Must get this from a real compactification.
Matias, CB
Dark Energy 2007
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
• SLED predicts there are 6D massless fermions in the bulk, as well as their properties• Massless, chiral, etc.
• Masses and mixings can be naturally achieved which agree with data! • Sterile bounds;
oscillation experiments;
• Lightest 3 states can have acceptable 3-flavour mixings.
• Active sterile mixings can satisfy incoherent bounds provided g ~ 10-4 or less (i ~ g/ci).
2
ii
aiU 223
1
cos
Matias, CB
Dark Energy 2007
Observational Consequences
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
• Energy loss into extra dimensions is close to existing bounds• Supernova, red-giant
stars,…
• Scalar-tensor form for gravity may have astrophysical implications.• Binary pulsars;…