Budapest 2007 Extra Dimensions and the Cosmological Constant Problem Cliff Burgess

Budapest 2007

Extra Dimensions and the Cosmological Constant Problem

Cliff Burgess

Budapest 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:• A. Albrecht, F. Ravndal, C. Skordis

Budapest 2007

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

Budapest 2007

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.

Budapest 2007

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.

HHmLSM*2 + dimensionless

Budapest 2007

Naturalness



M ~ 1011 GeV

Mw102 GeV

Mp ~1018 GeV

20

2 mm

221

2 Mkmm

BUT: effective theory can be defined at many scales

Hierarchy Problem: These must cancel to 20 digits!!

Budapest 2007

Naturalness


HHLSM*2 + dimensionless

Hierarchy problem: Since the largest mass dominates, why isn’t m ~ MGUT or Mp ??

• 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 ~ MB

2 – MF2

Extra Dimensions: the fundamental scale is much smaller than Mp , much as

GF-1/2 > Mw

Budapest 2007

Naturalness in Crisis


• The Standard Model’s dirty secret: there are really two unnaturally small terms.


Budapest 2007




me ~ 106 eV

m10-2 eV

mw ~1011 eV

m ~ 108 eV

440

4 mk

4441

4 mkmk ee

Can apply same argument to scales between TeV and sub-eV scales.

Cosmological Constant Problem: Must cancel to 32 decimal places!!

Budapest 2007



• The Standard Model’s dirty secret: there are really two unnaturally small terms.


Harder than the Hierarchy problem:

Integrating out the electron already gives too large a contribution!!

Budapest 2007


• 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?

Budapest 2007




Cosmological constant problem: Why is ~ 10-3 eV rather than me , Mw , MGUT or Mp?

• Approaches to solve the Hierarchy problem at ~ 10-2 eV?

Compositeness: graviton is not fundamental at energies E À Supersymmetry: there are new particles at E À and a symmetry which ensures cancellations so 2 ~ MB

2 – MF2

Extra Dimensions: the fundamental scale is much smaller than Mp

??

Budapest 2007

The Plan

• The Cosmological Constant problem• Technical Naturalness in Crisis





Budapest 2007

How Extra Dimensions Help

• 4D CC vs 4D vacuum energy

• Branes and scales

Budapest 2007




A cosmological constant is not distinguishable* from a Lorentz invariant vacuum energy

vs

gGTGG 488

TGgG 8

* in 4 dimensions…

Budapest 2007




In higher dimensions a 4D vacuum energy, if localized in the extra dimensions, can curve the extra dimensions instead of the observed four.

Chen, Luty & PontonArkani-Hamad et al

Kachru et al,Carroll & Guica

Aghababaie, et al

xtT NMMN2

Budapest 2007




These scales are natural using standard 4D arguments.

m ~ mw2/Mp

~ 10-2 eV

H ~ m2/Mp

mw Extra dimensions

could start here, if there are only two of them.

Arkani Hamed, Dvali, Dimopoulos

Budapest 2007




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!

Budapest 2007

The Plan

• The Cosmological Constant problem• Naturalness in Crisis





Budapest 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

Budapest 2007

The SLED Proposal



• 6D gravity scale: Mg ~ 10 TeV

• KK scale: 1/r ~ 10-2 eV

• Planck scale: Mp ~ Mg2 r

Arkani-Hamad, Dimopoulos & Dvali

Budapest 2007



The SLED Proposal




• Choose bulk to be supersymmetric(no 6D CC allowed)

Nishino & Sezgin

Budapest 2007



The SLED Proposal




• SUSY Breaking on brane: TeVin bulk: Mg

2/Mp ~1/r

Budapest 2007

The SLED Proposal

4D graviton

m ~ Mw2/Mp

H ~ m2/Mp

Mw

Particle Spectrum:

4D scalar: e r2 ~ const

SM on brane – no partners

Many KK modes in bulk

Budapest 2007

The SLED Proposal

4D graviton

m ~ Mw2/Mp

H ~ m2/Mp

Mw

Particle Spectrum:

4D scalar: e r2 ~ const

SM on brane – no partners

Many KK modes in bulk

Classical flat direction due to a scale invariance of the classical equations

NOT self-tuning: response to a kick is runaway along flat direction.

Budapest 2007

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?

Budapest 2007






• 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?

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• What is special about the ones which are 4D flat?

Budapest 2007








• What is special about the ones which are 4D flat?• Chiral gauged supergravity chosen

to allow extra dimensions topology of a sphere (only positive tensions):

RgxTGb

b2d

4

14

Budapest 2007






• 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().• dT/d nonzero implies curvature singularity

TgxS 4d

Budapest 2007






• 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.

Tolley, CB, Hoover & Aghababaie

Tolley, CB, de Rham & HooverCB, Hoover & Tasinato

Gibbons, Guvens & Pope

Budapest 2007






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

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• Conical singularities require vanishing dilaton coupling to branes (and hence scale invariant)

Budapest 2007








• Brane loops on their own cannot generate dilaton couplings from scratch.

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• Bulk loops can generate brane-dilaton coupling but TeV scale modes are suppressed at one loop by 6D supersymmetry

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• 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 e ~ 1/r2 and so only a few loops must be checked…..

Budapest 2007

The Plan

• The Cosmological Constant problem• Why is it so hard?



• Prognosis• Technical worries• Observational tests

Budapest 2007

Prognosis

• Theoretical worries


Budapest 2007

The Worries

• ‘Technical Naturalness’

• Runaway Behaviour

• Stabilizing the Extra Dimensions

• Famous No-Go Arguments

• Problems with Cosmology

• Constraints on Light Scalars

Budapest 2007

The Worries







Budapest 2007

The Worries







• 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

Budapest 2007

The Worries







• 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

Budapest 2007

Observational Consequences

• Quintessence cosmology

• Modifications to gravity

• Collider physics

• Neutrino physics?

• And more!

SUSY broken at

the TeV scale,

but not the MSSM!

Budapest 2007





• 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

Budapest 2007






• 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

Ms

MKK

Mg

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• Astrophysics



• Dimensionless couplings to bulk scalars are unsuppressed by Mg

Budapest 2007

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…

Budapest 2007

Detailed Worries and Observations










• Neutrino physics?

Budapest 2007

Backup slides

Budapest 2007

The Worries







Budapest 2007

The Worries







• 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

Budapest 2007

The Worries






• 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

Budapest 2007

The Worries






• Constraints on Light Scalars ]exp[)( 2 cbaV

42 1

)](log)log([r

rMcrMbaV

2

22

r

rML pkin

)/exp(0' baMrifV



Albrecht, CB, Ravndal, Skordis

Hubble damping can allow potential domination for exponentially large r, even though r is not stabilized.

Budapest 2007

The Worries







Budapest 2007

The Worries







• Why isn’t 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

Nilles et alCline et al

Erlich et al

Budapest 2007

The Worries










T1 + T2 = 0


Erlich et al

W(x)

W(x)

Budapest 2007

The Worries










T1 + T2 = 0


Erlich et al

• 6D analog corresponds to the Euler number topological constraint:

RgxTGb

b2d

4

14

Budapest 2007

The Worries










T1 + T2 = 0


Erlich et al

• 6D analog corresponds to the Euler number topological constraint:

RgxTGb

b2d

4

14

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

Budapest 2007

The Worries







• 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

Budapest 2007

The Worries









Budapest 2007

The Worries









4

Budapest 2007

The Worries







• 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.

Budapest 2007

The Worries







• 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 greater than the cutoff in an adiabatic way:

eVeff4 implies 42

Budapest 2007

The Worries







Budapest 2007

The Worries







• Post BBN:

Since r controls Newton’s constant, its motion between BBN and now will cause unacceptably large changes to G.

Budapest 2007

The Worries







• Post BBN:


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.

Budapest 2007

The Worries







• Post BBN:


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

Budapest 2007

The Worries







• 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

Budapest 2007

The Worries







• 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

Budapest 2007

The Worries







Budapest 2007

The Worries







• A light scalar with mass m ~ H has several generic difficulties:

What protects such a small mass from large quantum corrections?

Budapest 2007

The Worries








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.

Budapest 2007

The Worries








Isn’t such a light scalar already ruled out by precision tests of GR in the solar system?

Budapest 2007

The Worries









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.

Budapest 2007

The Worries









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

Budapest 2007

The Worries








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.)

Budapest 2007

The Worries








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.

Budapest 2007






• Astrophysics

Budapest 2007






• 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

Budapest 2007










• Astrophysics

Albrecht, CB, Ravndal & Skordis

]exp[)( 2 cbaV

42 1

)](log)log([r

rMcrMbaV

2

22

r

rML pkin

)/exp(0' baMrifV



Budapest 2007










• Astrophysics


log vs log a

Radiation

Matter

Total Scalar

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• Astrophysics


Radiation

Matter

Total Scalar

w Parameter:

andw vs log a

~ 0.7

w ~ – 0.9

m ~ 0.25

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• Astrophysics


vs log a

03.0

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• Astrophysics


log r vs log a

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• 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.

Budapest 2007






• 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.

Budapest 2007






• Astrophysics





Budapest 2007






• Astrophysics



• Dimensionless couplings to bulk scalars are unsuppressed by Mg

Ms

MKK

Mg

Budapest 2007






• Astrophysics





byxHHxdaS ,*4

Dimensionless coupling! O(0.1-0.001) from loops

Azuelos, Beauchemin & CB

Budapest 2007






• Astrophysics





byxHHxdaS ,*4

Dimensionless coupling! O(0.1-0.001) from loops


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

Budapest 2007






• Astrophysics






• Standard Model backgrounds

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• Astrophysics






Budapest 2007






• Astrophysics






• Significance of signal vs cut on missing ET

Budapest 2007






• Astrophysics






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

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• 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

Budapest 2007






• Astrophysics


• 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

Budapest 2007






• Astrophysics




bauiiau yxNHLxdS ,4

Dimensionful coupling ~ 1/Mg

Matias, CB

Budapest 2007






• Astrophysics




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

Budapest 2007






• Astrophysics




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

Budapest 2007






• Astrophysics




t

bauiiau yxNHLxdS ,4


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

Budapest 2007






• Astrophysics




t

bauiiau yxNHLxdS ,4


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

Budapest 2007






• Astrophysics




• 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

Budapest 2007






• Astrophysics




• 1 massless state• 2 next- lightest states

have strong overlap with brane.• Inverted hierarchy.

• Massive KK states mix weakly.

Matias, CB

Budapest 2007






• Astrophysics




• 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

Budapest 2007






• Astrophysics




• 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

Budapest 2007






• 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;…

Documents

Budapest 2007 Extra Dimensions and the Cosmological Constant Problem Cliff Burgess