Extra Dimensions and the Cosmological Constant Problem

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




Concordance cosmology points to several types of cosmic ‘matter’:

mDMDE TTTGG 8

mni

ii

gpT

0

0

0 mDM pp

Dark Energy 2007




w = pDE/D for a cosmological constant

N. Wright, astro-ph/0701584

Dark Energy 2007


• 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


• 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




Dark Energy 2007




The observed dark energy density corresponds to a very small vacuum energy:

implies

329534 cm/g10/ c

V10 2 e

Dark Energy 2007




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




42 V10 e

me ~ 106 eV

m10-2 eV

mw ~1011 eV

m ~ 108 eV

40 mk


Dark Energy 2007




42 V10 e

me ~ 106 eV

m10-2 eV

mw ~1011 eV

m ~ 108 eV

40 mk

441 mkmk ee


Dark Energy 2007




42 V10 e

me ~ 106 eV

m10-2 eV

mw ~1011 eV

m ~ 108 eV

40 mk

441 mkmk ee


Must cancel to 32 decimal places!!

Dark Energy 2007




42 V10 e

me ~ 106 eV

m10-2 eV

mw ~1011 eV

m ~ 108 eV

441 mkmk ee


...442 ee mkmk

40 mk

Dark Energy 2007




42 V10 e

me ~ 106 eV

m10-2 eV

mw ~1011 eV

m ~ 108 eV

441 mkmk ee


...442 ee mkmk

40 mk

Must cancel to 40 decimal places!!

Dark Energy 2007




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



is a constant if it is vacuum energy

Dark Energy 2007




More complicated time-dependence is possible

Dark Energy 2007




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






Dark Energy 2007

How Extra Dimensions Help

• 4D CC vs 4D vacuum energy

• Branes and scales

Dark Energy 2007




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




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



• 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




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




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



• Branes and scales These scales are natural using standard 4D arguments.

m ~ mw2/Mp

~ 10-2 eV

H ~ m2/Mp

mw

Dark Energy 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!

Dark Energy 2007

The Plan






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 6D CC



• Several 6D SUGRAs are known, including chiral and non-chiral variants. • None have a 6D CC.

Dark Energy 2007


• The 6D CC



• Several 6D SUGRAs are known, including chiral and non-chiral variants.• None have a 6D CC.

Nishino & Sezgin

Dark Energy 2007


• The 6D CC



• Generates large 4D vacuum energy

• This energy is localized in the extra dimensions (plus higher-derivatives)

ii

i yyT 2

Dark Energy 2007


• The 6D CC



• Solve classical equations in presence of branes

• Plug back into action

smoothii

i RyyTR 2

Dark Energy 2007


• The 6D CC





...2 RgydTi

ieff

smoothii

i RyyTR 2

Dark Energy 2007


• The 6D CC





...2 RgydTi

ieff

smoothii

i RyyTR 2

Tensions cancel between brane and bulk!!

Chen, Luty & Ponton

Dark Energy 2007


• The 6D CC





...2 RgydTi

ieff

smoothii

i RyyTR 2

Smooth parts also cancel for supersymmetric theories!!

Aghababaie et al.

Dark Energy 2007


• The 6D CC



• 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




• Prognosis• Technical worries• Observational tests

Dark Energy 2007

Prognosis

• Theoretical worries


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







Dark Energy 2007

The Worries







• 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







• 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







• 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







Dark Energy 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

Dark Energy 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

Dark Energy 2007

Prognosis

• Theoretical worries


Dark Energy 2007

The Observational Tests

• Quintessence cosmology

Dark Energy 2007



• Modifications to gravity

Dark Energy 2007




• Collider physics

Dark Energy 2007




• Collider physics SUSY broken at the TeV scale,

but not the MSSM!

Dark Energy 2007





• Neutrino physics?

Dark Energy 2007






• 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


• 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




• Tuned initial conditions• Much like for the Hot Big Bang Model.

Dark Energy 2007

Summary




• 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











Dark Energy 2007

Backup slides

Dark Energy 2007

The Worries







Dark Energy 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

Dark Energy 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

Dark Energy 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.

Dark Energy 2007

The Worries







Dark Energy 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

Dark Energy 2007

The Worries









Dark Energy 2007

The Worries









4

Dark Energy 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.

Dark Energy 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 \mu greater than the cutoff in an adiabatic way:

eVeff4 implies 42

Dark Energy 2007

The Worries







Dark Energy 2007

The Worries







• 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







• 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.

Dark Energy 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

Dark Energy 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

Dark Energy 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

Dark Energy 2007

The Worries







Dark Energy 2007

The Worries







• 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








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








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

Dark Energy 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.

Dark Energy 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

Dark Energy 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.)

Dark Energy 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.

Dark Energy 2007

Observational Consequences




• Neutrino physics

• Astrophysics

Dark Energy 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

Dark Energy 2007










• Astrophysics

Albrecht, CB, Ravndal & Skordis

]exp[)( 2 cbaV

42 1

)](log)log([r

rMcrMbaV

2

22

r

rML pkin

)/exp(0' baMrifV



Dark Energy 2007










• Astrophysics


log vs log a

Radiation

Matter

Total Scalar

Dark Energy 2007










• Astrophysics


Radiation

Matter

Total Scalar

w Parameter:

andw vs log a

~ 0.7

w ~ – 0.9

m ~ 0.25

Dark Energy 2007










• Astrophysics


vs log a

03.0

Dark Energy 2007










• Astrophysics


log r vs log a

Dark Energy 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.

Dark Energy 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.

Dark Energy 2007






• 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






• 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






• Astrophysics





byxHHxdaS ,*4

Dimensionless coupling! O(0.1-0.001) from loops

Azuelos, Beauchemin & CB

Dark Energy 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.

Dark Energy 2007






• Astrophysics






• Standard Model backgrounds

Dark Energy 2007






• Astrophysics






Dark Energy 2007






• Astrophysics






• Significance of signal vs cut on missing ET

Dark Energy 2007






• Astrophysics






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

Dark Energy 2007






• 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






• 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

Dark Energy 2007






• Astrophysics




bauiiau yxNHLxdS ,4

Dimensionful coupling ~ 1/Mg

Matias, CB

Dark Energy 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

Dark Energy 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

Dark Energy 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

Dark Energy 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

Dark Energy 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

Dark Energy 2007






• Astrophysics




• 1 massless state• 2 next- lightest states

have strong overlap with brane.• Inverted hierarchy.

• Massive KK states mix weakly.

Matias, CB

Dark Energy 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

Dark Energy 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

Dark Energy 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

Extra Dimensions and the Cosmological Constant Problem