The Cosmological Constant on the Brane New Approaches to Naturalness Cliff Burgess

The Cosmological Constant on the Brane

New Approaches

to Naturalness

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:

G. Azuelos, P.-H. Beauchemin, J. Matias, F. Quevedo

Cosmology:

A. Albrecht, F. Ravndal, C. Skordis

The Plan

• Naturalness and Cosmology• Why naturalness is an important criterion

• 4D Dark Energy from 6D Supergravity• Changing how the vacuum energy gravitates.• Supersymmetric Large Extra Dimensions (SLED)

• Have we been MSLED?• Cosmology; Colliders; Newton’s Law; Neutrino

Oscillations…

Naturalness and Dark Energy

• Why doesn’t the electron contribute too large a zero-point energy to the cosmological constant?

43obs eV)10(

Technical Naturalness

• Given a small quantity = 0 +

• In the fundamental theory, why should 0 be small?

• Given that 0 is small, why does it stay small as one integrates out physics up to the scales for which is measured?

This may have to wait until we know the fundamental theory.

This is serious because it involves physics we think we understand…

Scales

These scales are natural using standard 4D arguments.

How can these scales be changed to reduce the vacuum energy’s gravity?

Vacuum Energy & 4D Curvature

• In 4D a Lorentz-invariant vacuum energy necessarily gravitates like a cosmological constant.

• In higher dimensions a 4D vacuum energy on a brane can curve the extra dimensions instead of the observed 4 dimensions.

Arkani-Hamad et alKachru et al,

Carroll & GuicaAghababaie, et al

The SLED Proposal

• Suppose physics is extra-dimensional above the 10-2 eV scale.

• Suppose the physics of the bulk is supersymmetric.

The SLED Proposal



• Experimentally possible:• There are precisely two

extra dimensions at these scales;

• We are brane bound;

The SLED Proposal



• Experimentally possible:• There are precisely two

extra dimensions at these scales;

• We are brane bound;

• The 6D gravity scale is in the TeV region.

rMM gp2

The SLED Proposal



• Experimentally possible provided:• SUSY breaks at scale Mg

on the branes;

• Trickle-down of SUSY breaking to the bulk is:

rM

Mm

p

gSB

12

Scales

These scales are natural using standard 4D arguments.

Naturalness for these scales must be rethought in 6D.

The CC Problem in 6D

• The 6D CC

• Integrate out brane physics

• Integrate out bulk physics• Classical contribution• Quantum corrections


• The 6D CC



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


• The 6D CC



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

Nishino & Sezgin


• The 6D CC



• Generates large 4D vacuum energy

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

ii

i yyT 2


• The 6D CC



• Solve classical equations in presence of branes

• Plug back into action

smoothii

i RyyTR 2


• The 6D CC





...2 RgydTi

ieff

smoothii

i RyyTR 2

Tensions cancel between brane and bulk!!

Chen, Luty & Ponton


• The 6D CC





...2 RgydTi

ieff

smoothii

i RyyTR 2

Smooth parts also cancel for supersymmetric theories!!

Aghababaie et al.


• 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

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?






• Search for solutions to 6D supergravity: • What bulk geometry

arises from a given brane configuration?






• Search for solutions to 6D supergravity: • What kind of bulk

geometry arises from a given pair of branes?

6D Solutions: No Branes

• Salam Sezgin ansatz: maximal symmetry in 4D and in 2D

ds2 = g dx dx + gmn dym dyn

F = f mn dym dyn ; m = 0


• Salam Sezgin ansatz: maximal symmetry in 4D and in 2D

ds2 = g dx dx + gmn dym dyn

F = f mn dym dyn ; m = 0• Implies:

1. g = 2. spherical extra dimensions 3. dilaton stabilization:

g2 e = 1/r2

S2


• Why a flat solution?

80’s: Unit magnetic flux leaves SUSY

unbroken…


• Why a flat solution?

80’s: Unit magnetic flux leaves SUSY

unbroken…

…but: turns out to be 4D flat for higher fluxes as well!

6D Solutions: Rugby Balls

• Can include branes: Cut-and-paste solutions have equal-sized conical singularities at both poles;

Interpret singularity as due to back reaction of branes located at this position

Solutions break supersymmetry

Aghababaie, CB, Parameswaran & Quevedo

6D Solutions: Conical Singularities

• General solutions with two conical singularities:

Unequal conical defects lead to warped geometries in the bulk;

All such (static) solutions have flat 4D geometries

Gibbons, Guven & Pope

Aghababaie, CB, Cline, Firouzjahi, Parameswaran, Quevedo

Tasinato & Zavala

6D Solutions: GGP solutions

• General solutions with flat 4D geometry:Solutions need not have purely conical singularities at brane positions;Non-conical singularities arise when the dilaton diverges near the branes

Gibbons, Guven & Pope

6D Solutions: Asymptotic forms

• General near-brane asymptotic behaviour:

Solutions take power-law near-brane form as a function of the proper distance, , to the brane

Field equations imply ‘Kasner-like’ relations amongst the powers:

p - = + 3 + = 2 + 3 2 + 2 + p2 = 1

Lorentz invariant if: =

Tolley, CB, Hoover & Aghababaie

6D Solutions: Brane matching

• Near-brane asymptotics and brane properties:

Powers may be related to averaged conserved currents if the singular behaviour is regulated using a ‘thick brane’

Navarro & SantiagoTolley, CB, de Rham & Hoover

6D Solutions: Other static solutions

• Solutions with dS and AdS 4D geometry:

Asymptotic form at one brane dictated by that at the other brane;

Solutions cannot have purely conical singularities at both brane positions;

• Static Lorentz-breaking solutions ( ):

Static solutions exist for which the time and space parts of the 4D metric vary differently within the bulk;

Tolley, CB, Hoover & Aghababaie

6D Solutions: Time-dependence

• Linearized perturbationsExplicit solutions are possible for conical geometries in terms of Hypergeometric functions: Solutions are marginally stable, if the perturbations are not too singular at the brane positions;

• Nonlinear Plane-Wave Solutions:Describe eg passage of bubble-nucleation wall along the brane;

Tolley, CB, de Rham & Hoover

6D Solutions: Scaling solutions

• A broad class of exact scaling solutions Exact time-dependent solutions are possible subject to the assumption of a scaling ansatz:

Likely to describe the late-time attractor behaviour of time dependent evolution;

Most of these solutions describe rapid runaways with rapidly growing or shrinking dimensions.

Tolley, CB, de Rham & HooverCopeland & Seto






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

• Conical singularities require vanishing dilaton coupling to branes.

• Brane loops cannot generate dilaton couplings from scratch.

• Bulk loops are SUSY suppressed.

What About Weinberg’s Theorem?

• Weinberg has a general objection to self-tuning mechanisms for solving the cosmological constant problem.







4 V

Observational Consequences

• Quintessence cosmology

• Modifications to gravity

• Collider physics

• Neutrino physics

• Astrophysics






• 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










• 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:










• Astrophysics


log vs log a

Radiation

Matter

Total Scalar










• Astrophysics


Radiation

Matter

Total Scalar

w Parameter:

andw vs log a

~ 0.7

w ~ – 0.9

m ~ 0.25










• Astrophysics


vs log a

03.0










• Astrophysics


log r vs log a






• 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.






• 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.






• 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






• Astrophysics





byxHHxdaS ,*4

Dimensionless coupling! O(0.1-0.001) from loops

Azuelos, Beauchemin & CB






• Astrophysics





byxHHxdaS ,*4

Dimensionless coupling! O(0.1-0.001) from loops







• Astrophysics











• Astrophysics











• 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 & London






• Astrophysics


• Masses and mixings can be naturally achieved which agree with data! • Sterile bounds;

oscillation experiments;

Matias, CB & London

• 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






• Astrophysics




Matias, CB & London

bauiiau yxNHLxdS ,4

Dimensionful coupling ~ 1/Mg






• Astrophysics




Matias, CB & London

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;






• Astrophysics




Matias, CB & London

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






• Astrophysics




Matias, CB & London

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.






• Astrophysics




Matias, CB & London

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 < 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.






• Astrophysics




Matias, CB & London

• 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






• Astrophysics




Matias, CB & London

• 1 massless state• 2 next- lightest states

have strong overlap with brane.• Inverted hierarchy.

• Massive KK states mix weakly.






• Astrophysics




Matias, CB & London

• 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.






• Astrophysics




Matias, CB & London

• 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






• 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;…

Current Worries

• Technically natural brane choices• Runaway solutions and initial conditions.• What controls scalar-tensor bounds. • How contrived is post-BBN cosmology?

(Robustness to initial conditions, etc) • Large-extra dimensional pre-BBN cosmology?• Dynamics of volume and warping.• Connection to string theory?

Documents

The Cosmological Constant on the Brane New Approaches to Naturalness Cliff Burgess