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

Quevedo - Cosmology
- A. Albrecht, F. Ravndal, C. Skordis

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

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.

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.

dimensionless

Naturalness

BUT effective theory can be defined at many

scales

- Ideas for what lies beyond the Standard Model are

largely driven by technical naturalness. - Motivated by belief that SM is an effective field

theory.

dimensionless

Hierarchy Problem These must cancel to 20

digits!!

Naturalness

- 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

MB2 MF2 - Extra Dimensions the fundamental scale is much

smaller than Mp , much as GF-1/2 gt Mw

- Ideas for what lies beyond the Standard Model are

largely driven by technical naturalness. - Motivated by belief that SM is an effective field

theory.

dimensionless

Hierarchy problem Since the largest mass

dominates, why isnt m MGUT or Mp ??

Naturalness in Crisis

- Ideas for what lies beyond the Standard Model are

largely driven by technical naturalness. - Motivated by belief that SM is an effective field

theory. - The Standard Models dirty secret there are

really two unnaturally small terms.

dimensionless

Naturalness in Crisis

- Ideas for what lies beyond the Standard Model are

largely driven by technical naturalness. - Motivated by belief that SM is an effective field

theory.

Can apply same argument to scales between TeV

and sub-eV scales.

dimensionless

Cosmological Constant Problem Must cancel to 32

decimal places!!

Naturalness in Crisis

- Ideas for what lies beyond the Standard Model are

largely driven by technical naturalness. - Motivated by belief that SM is an effective field

theory. - The Standard Models dirty secret there are

really two unnaturally small terms.

Harder than the Hierarchy problem

Integrating out the electron already gives too

large a contribution!!

dimensionless

Naturalness in Crisis

- Dark energy vs vacuum energy
- Why must the vacuum energy be large?

Seek to change properties of low-energy

particles (like the electron) so that their

zero-point energy does not gravitate, even though

quantum effects do gravitate in atoms!

Why this? But not this?

Naturalness in Crisis

- Approaches to solve the Hierarchy problem at m

10-2 eV? - Compositeness graviton is not fundamental at

energies E À m - Supersymmetry there are new particles at E À m

and a symmetry which ensures cancellations so m2

MB2 MF2 - Extra Dimensions the fundamental scale is much

smaller than Mp

- Ideas for what lies beyond the Standard Model are

largely driven by technical naturalness. - Motivated by belief that SM is an effective field

theory.

dimensionless

??

Cosmological constant problem Why is

m 10-3 eV rather than me , Mw , MGUT or Mp?

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

How Extra Dimensions Help

- 4D CC vs 4D vacuum energy
- Branes and scales

How Extra Dimensions Help

- 4D CC vs 4D vacuum energy
- Branes and scales

A cosmological constant is not distinguishable

from a Lorentz invariant vacuum energy vs

in 4 dimensions

How Extra Dimensions Help

In higher dimensions a 4D vacuum energy, if

localized in the extra dimensions, can curve the

extra dimensions instead of the observed four.

- 4D CC vs 4D vacuum energy
- Branes and scales

Chen, Luty Ponton Arkani-Hamad et al Kachru et

al, Carroll Guica Aghababaie, et al

How Extra Dimensions Help

Arkani Hamed, Dvali, Dimopoulos

Extra dimensions could start here, if there

are only two of them.

- 4D CC vs 4D vacuum energy
- Branes and scales

These scales are natural using standard 4D

arguments.

How Extra Dimensions Help

Must rethink how the vacuum gravitates in 6D

for these scales. SM interactions do not

change at all!

- 4D CC vs 4D vacuum energy
- Branes and scales

Only gravity gets modified over the most

dangerous distance scales!

The Plan

- The Cosmological Constant problem
- 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

The SLED Proposal

Aghababaie, CB, Parameswaran Quevedo

- Suppose physics is extra-dimensional above the

10-2 eV scale. - Suppose the physics of the bulk is supersymmetric.

The SLED Proposal

Arkani-Hamad, Dimopoulos Dvali

- Suppose physics is extra-dimensional above the

10-2 eV scale. - Suppose the physics of the bulk is supersymmetric.

- 6D gravity scale Mg 10 TeV
- KK scale 1/r 10-2 eV
- Planck scale Mp Mg2 r

The SLED Proposal

Nishino Sezgin

- Suppose physics is extra-dimensional above the

10-2 eV scale. - Suppose the physics of the bulk is supersymmetric.

- 6D gravity scale Mg 10 TeV
- KK scale 1/r 10-2 eV
- Planck scale Mp Mg2 r
- Choose bulk to be supersymmetric (no 6D CC

allowed)

The SLED Proposal

- Suppose physics is extra-dimensional above the

10-2 eV scale. - Suppose the physics of the bulk is supersymmetric.

- 6D gravity scale Mg 10 TeV
- KK scale 1/r 10-2 eV
- Planck scale Mp Mg2 r
- SUSY Breaking on brane TeV in bulk Mg2/Mp

1/r

The SLED Proposal

Particle Spectrum

SM on brane no partners Many KK modes

in bulk

4D scalar ef r2 const

4D graviton

The SLED Proposal

Particle Spectrum

Classical flat direction due to a scale

invariance of the classical equations NOT

self-tuning response to a kick is runaway along

flat direction.

SM on brane no partners Many KK modes

in bulk

4D scalar ef r2 const

4D graviton

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?

What Needs Understanding

- 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?

- 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?

What Needs Understanding

- 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?

- 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?

What Needs Understanding

- 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?

- 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?

- Chiral gauged supergravity chosen to allow extra

dimensions topology of a sphere (only positive

tensions)

What Needs Understanding

- 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(f). - dT/df nonzero implies curvature singularity

- 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?

What Needs Understanding

- 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.

- 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?

Gibbons, Guvens Pope

Tolley, CB, Hoover Aghababaie Tolley, CB, de

Rham Hoover CB, Hoover Tasinato

What Needs Understanding

Gibbons, Guven Pope

- 4D CC vs 4D vacuum energy
- Branes and scales

- Most general 4D flat solutions to chiral 6D

supergravity, without matter fields. - l3 nonzero gives curvature singularities at

branes

6D Solutions No Branes

- Salam Sezgin ansatz maximal symmetry in 4D

and in 2D - ds2 gmn dxm dxn gmn dym dyn
- F f emn dym dyn m f 0

6D Solutions No Branes

- Salam Sezgin ansatz maximal symmetry in 4D

and in 2D - ds2 gmn dxm dxn gmn dym dyn
- F f emn dym dyn m f 0
- Implies
- 1. gmn hmn
- 2. spherical extra dimensions
- 3. dilaton stabilization
- g2 ef 1/r2

6D Solutions No Branes

- Why a flat solution?
- 80s Unit magnetic flux leaves SUSY
- unbroken

6D Solutions No Branes

- Why a flat solution?
- 80s Unit magnetic flux leaves SUSY
- unbroken
- but turns out to be 4D flat for

higher fluxes as well!

6D Solutions Rugby Balls

Aghababaie, CB, Parameswaran Quevedo

- 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

6D Solutions Conical Singularities

Gibbons, Guven Pope Aghababaie, CB, Cline,

Firouzjahi, Parameswaran, Quevedo Tasinato

Zavala

- General solns with two conical singularities
- Unequal defects have warped geometries in the

bulk - Conical singularities correspond to absence of

brane coupling to 6D dilaton (and preserve bulk

scale invariance) - All such (static) solutions have flat 4D

geometries

6D Solutions GGP solutions

Gibbons, Guven Pope

- 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

6D Solutions Asymptotic forms

Tolley, CB, Hoover Aghababaie

- General near-brane asymptotic behaviour
- Solutions take power-law near-brane form as a

function of the proper distance, r, to the brane - Field equations imply Kasner-like relations

amongst the powers p - g w 3 a

b w2 3 a2 b2 p2 1 - Lorentz invariant if w a

6D Solutions Brane matching

Navarro Santiago Tolley, CB, de Rham Hoover

- Near-brane asymptotics and brane properties
- Powers may be related to averaged conserved

currents if the singular behaviour is regulated

using a thick brane

6D Solutions Other static solutions

Tolley, CB, Hoover Aghababaie

- 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 (a ¹ w)
- Static solutions exist for which the time and

space parts of the 4D metric vary differently

within the bulk

6D Solutions Time-dependence

Cline Vinet Tolley, CB, de Rham Hoover Lee

Papazoglou

- Linearized perturbations
- Explicit 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

6D Solutions Time-dependence

Tolley et al Kaloper et al

- Nonlinear Plane-Wave Solutions
- Describe eg passage of bubble-nucleation

wall along the brane - Black Hole Solutions
- Conical defects threaded through bulk

black holes

6D Solutions Scaling solutions

Tolley, CB, de Rham Hoover Copeland Seto

- 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.

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

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?

What Needs Understanding

- When both branes have conical singularities all

static solutions have 4D minkowski geometry.

- 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?

What Needs Understanding

- When both branes have conical singularities all

static solutions have 4D minkowski geometry. - Conical singularities require vanishing dilaton

coupling to branes (and hence scale invariant)

- 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?

What Needs Understanding

- When both branes have conical singularities all

static solutions have 4D minkowski geometry. - Conical singularities require vanishing dilaton

coupling to branes (and hence scale invariant) - Brane loops on their own cannot generate dilaton

couplings from scratch.

- 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?

What Needs Understanding

- When both branes have conical singularities all

static solutions have 4D minkowski geometry. - Conical singularities require vanishing dilaton

coupling to branes (and hence scale invariant) - Brane loops on their own cannot generate dilaton

couplings from scratch. - Bulk loops can generate brane-dilaton coupling

but TeV scale modes are suppressed at one loop by

6D supersymmetry

- 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?

What Needs Understanding

- When both branes have conical singularities all

static solutions have 4D minkowski geometry. - Conical singularities require vanishing dilaton

coupling to branes (and hence scale invariant) - Brane loops on their own cannot generate dilaton

couplings from scratch. - 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 ef 1/r2 and so

only a few loops must be checked..

- 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?

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

Prognosis

- Theoretical worries
- Observational tests

The Worries

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

The Worries

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

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?

The Worries

Tolley, CB, Hoover Aghababaie Tolley, CB, de

Rham Hoover CB, Hoover Tasinato

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

- Classical part of the argument
- What choices must be made to ensure 4D flatness?

- Now understand how 2 extra dimensions respond to

presence of 2 branes having arbitrary couplings. - Not all are flat in 4D, but all of those having

only conical singularities are flat. - (Conical singularities correspond to absence

of dilaton couplings to branes)

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

The Worries

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

The Worries

Albrecht, CB, Ravndal, Skordis Tolley, CB,

Hoover Aghababaie Tolley, CB, de Rham Hoover

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

- Most brane properties and initial conditions do

not lead to anything like the universe we see

around us. - For many choices the extra dimensions implode or

expand to infinite size.

The Worries

Albrecht, CB, Ravndal, Skordis Tolley, CB,

Hoover Aghababaie Tolley, CB, de Rham Hoover

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

- Most brane properties and initial conditions do

not lead to anything like the universe we see

around us. - For many choices the extra dimensions implode or

expand to infinite size. - Initial condition problem much like the Hot Big

Bang, possibly understood by reference to earlier

epochs of cosmology (eg inflation)

Prognosis

- Theoretical worries
- Observational tests

Observational Consequences

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics?
- And more!

SUSY broken at the TeV scale,

but not the MSSM!

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

Observational Consequences

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- Can there be observable signals if Mg 10 TeV?
- Must hit new states before E Mg . Eg string

and KK states have MKK lt Ms lt Mg

Observational Consequences

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- Can there be observable signals if Mg 10 TeV?
- Must hit new states before E Mg . Eg string

and KK states have MKK lt Ms lt Mg - Dimensionless couplings to bulk scalars are

unsuppressed by Mg

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

Detailed Worries and Observations

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics?

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

Backup slides

The Worries

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

The Worries

Salam Sezgin

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

- Classical flat direction corresponding to

combination of radius and dilaton

ef r2 constant. - Loops lift this flat direction, and in so doing

give dynamics to f and r.

The Worries

Kantowski Milton Albrecht, CB, Ravndal, Skordis

CB Hoover Ghilencea, Hoover, CB Quevedo

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

Potential domination when

Canonical Variables

The Worries

Albrecht, CB, Ravndal, Skordis

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

Potential domination when

Hubble damping can allow potential domination

for exponentially large r, even though r is not

stabilized.

Canonical Variables

The Worries

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

The Worries

Nilles et al Cline et al Erlich et al

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

- Why isnt 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

The Worries

Nilles et al Cline et al Erlich et al

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

- Why isnt 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

The Worries

Nilles et al Cline et al Erlich et al

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

- Why isnt 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

- 6D analog corresponds to the Euler number

topological constraint

The Worries

Nilles et al Cline et al Erlich et al

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

- Why isnt 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

- 6D analog corresponds to the Euler number

topological constraint

- Being topological, this is preserved under

renormalization. If S Tb nonzero then R becomes

nonzero

The Worries

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

- Weinbergs No-Go Theorem
- Steven Weinberg has a general objection to

self-tuning mechanisms for solving the

cosmological constant problem that are based on

scale invariance

The Worries

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

- Weinbergs No-Go Theorem
- Steven Weinberg has a general objection to

self-tuning mechanisms for solving the

cosmological constant problem that are based on

scale invariance

The Worries

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

- Weinbergs No-Go Theorem
- Steven Weinberg has a general objection to

self-tuning mechanisms for solving the

cosmological constant problem that are based on

scale invariance

The Worries

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

- Nimas No-Go Argument
- One can have a vacuum energy m4 with m

greater than the cutoff, provided it is turned on

adiabatically. - So having extra dimensions with r 1/m does

not release one from having to find an

intrinsically 4D mechanism.

The Worries

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

- Nimas No-Go Argument
- One can have a vacuum energy m4 with m

greater than the cutoff, provided it is turned on

adiabatically. - So having extra dimensions with r 1/m does

not release one from having to find an

intrinsically 4D mechanism.

- Scale invariance precludes obtaining m greater

than the cutoff in an adiabatic way

implies

The Worries

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

The Worries

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

- Post BBN
- Since r controls Newtons constant, its

motion between BBN and now will cause

unacceptably large changes to G.

The Worries

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

- Post BBN
- Since r controls Newtons constant, its

motion between BBN and now will cause

unacceptably large changes to G. - Even if the kinetic energy associated with r

were to be as large as possible at BBN, Hubble

damping keeps it from rolling dangerously far

between then and now.

The Worries

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

- Post BBN
- Since r controls Newtons constant, its

motion between BBN and now will cause

unacceptably large changes to G. - Even if the kinetic energy associated with r

were to be as large as possible at BBN, Hubble

damping keeps it from rolling dangerously far

between then and now.

log r vs log a

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

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

The Worries

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

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?

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.

The Worries

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

- A light scalar with mass m H has several

generic difficulties - Isnt such a light scalar already ruled out

by precision tests of GR in the solar system?

The Worries

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

- A light scalar with mass m H has several

generic difficulties - Isnt such a light scalar already ruled out

by precision tests of GR in the solar system?

The same logarithmic corrections which enter the

potential can also appear in its matter

couplings, making them field dependent and so

also time-dependent as f rolls. Can arrange these

to be small here now.

The Worries

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

- A light scalar with mass m H has several

generic difficulties - Isnt such a light scalar already ruled out

by precision tests of GR in the solar system?

The same logarithmic corrections which enter the

potential can also appear in its matter

couplings, making them field dependent and so

also time-dependent as f rolls. Can arrange these

to be small here now.

a vs log a

The Worries

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

- A light scalar with mass m H has several

generic difficulties - Shouldnt there be strong bounds due to

energy losses from red giant stars and

supernovae? (Really a bound on LEDs and not on

scalars.)

The Worries

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

- A light scalar with mass m H has several

generic difficulties - Shouldnt there be strong bounds due to

energy losses from red giant stars and

supernovae? (Really a bound on LEDs and not on

scalars.) - Yes, and this is how the scale M 10 TeV for

gravity in the extra dimensions is obtained.

Observational Consequences

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

Observational Consequences

Albrecht, CB, Ravndal Skordis Kainulainen

Sunhede

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- Quantum vacuum energy lifts flat direction.
- Specific types of scalar interactions are

predicted. - Includes the Albrecht-Skordis type of potential
- Preliminary studies indicate it is possible to

have viable cosmology - Changing G BBN

Observational Consequences

Albrecht, CB, Ravndal Skordis

- Quantum vacuum energy lifts flat direction.
- Specific types of scalar interactions are

predicted. - Includes the Albrecht-Skordis type of potential
- Preliminary studies indicate it is possible to

have viable cosmology - Changing G BBN

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

Potential domination when

Canonical Variables

Observational Consequences

Albrecht, CB, Ravndal Skordis

Radiation Matter Total Scalar

- Quantum vacuum energy lifts flat direction.
- Specific types of scalar interactions are

predicted. - Includes the Albrecht-Skordis type of potential
- Preliminary studies indicate it is possible to

have viable cosmology - Changing G BBN

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

log r vs log a

Observational Consequences

Albrecht, CB, Ravndal Skordis

- L 0.7

- Quantum vacuum energy lifts flat direction.
- Specific types of scalar interactions are

predicted. - Includes the Albrecht-Skordis type of potential
- Preliminary studies indicate it is possible to

have viable cosmology - Changing G BBN

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- m 0.25

- and w
- vs log a

Radiation Matter Total Scalar w Parameter

w 0.9

Observational Consequences

Albrecht, CB, Ravndal Skordis

- Quantum vacuum energy lifts flat direction.
- Specific types of scalar interactions are

predicted. - Includes the Albrecht-Skordis type of potential
- Preliminary studies indicate it is possible to

have viable cosmology - Changing G BBN

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

a vs log a

Observational Consequences

Albrecht, CB, Ravndal Skordis

- Quantum vacuum energy lifts flat direction.
- Specific types of scalar interactions are

predicted. - Includes the Albrecht-Skordis type of potential
- Preliminary studies indicate it is possible to

have viable cosmology - Changing G BBN

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

log r vs log a

Observational Consequences

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- At small distances
- Changes Newtons Law at range r/2p 1 mm.
- At large distances
- Scalar-tensor theory out to distances of order

H0.

Observational Consequences

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- At small distances
- Changes Newtons Law at range r/2p 1 mm.
- At large distances
- Scalar-tensor theory out to distances of order

H0.

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

Observational Consequences

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- Can there be observable signals if Mg 10 TeV?
- Must hit new states before E Mg . Eg string

and KK states have MKK lt Ms lt Mg - Dimensionless couplings to bulk scalars are

unsuppressed by Mg

Observational Consequences

Azuelos, Beauchemin CB

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- Not the MSSM!
- No superpartners
- Bulk scale bounded by astrophysics
- Mg 10 TeV
- Many channels for losing energy to KK modes
- Scalars, fermions, vectors live in the bulk

Dimensionless coupling! O(0.1-0.001) from

loops

Observational Consequences

Azuelos, Beauchemin CB

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- Not the MSSM!
- No superpartners
- Bulk scale bounded by astrophysics
- Mg 10 TeV
- Many channels for losing energy to KK modes
- Scalars, fermions, vectors live in the bulk

Dimensionless coupling! O(0.1-0.001) from

loops

- Use H decay into gg, so search for two hard

photons plus missing ET.

Observational Consequences

Azuelos, Beauchemin CB

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- Not the MSSM!
- No superpartners
- Bulk scale bounded by astrophysics
- Mg 10 TeV
- Many channels for losing energy to KK modes
- Scalars, fermions, vectors live in the bulk

- Standard Model backgrounds

Observational Consequences

Azuelos, Beauchemin CB

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- Not the MSSM!
- No superpartners
- Bulk scale bounded by astrophysics
- Mg 10 TeV
- Many channels for losing energy to KK modes
- Scalars, fermions, vectors live in the bulk

Observational Consequences

Azuelos, Beauchemin CB

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- Not the MSSM!
- No superpartners
- Bulk scale bounded by astrophysics
- Mg 10 TeV
- Many channels for losing energy to KK modes
- Scalars, fermions, vectors live in the bulk

- Significance of signal vs cut on missing ET

Observational Consequences

Azuelos, Beauchemin CB

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- Not the MSSM!
- No superpartners
- Bulk scale bounded by astrophysics
- Mg 10 TeV
- Many channels for losing energy to KK modes
- Scalars, fermions, vectors live in the bulk

- Possibility of missing-ET cut improves the reach

of the search for Higgs through its gg channel

Observational Consequences

Matias, CB

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- SLED predicts there are 6D massless fermions in

the bulk, as well as their properties - Massless, chiral, etc.
- Masses and mixings can be chosen to agree with

oscillation data. - Most difficult bounds on resonant SN

oscillilations.

Observational Consequences

Matias, CB

- 6D supergravities have many bulk fermions
- Gravity (gmn, ym, Bmn, c, j)
- Gauge (Am, l)
- Hyper (F, x)
- Bulk couplings dictated by supersymmetry
- In particular 6D fermion masses must vanish
- Back-reaction removes KK zero modes
- eg boundary condition due to conical defect at

brane position

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- SLED predicts there are 6D massless fermions in

the bulk, as well as their properties - Massless, chiral, etc.
- Masses and mixings can be naturally achieved

which agree with data! - Sterile bounds oscillation experiments

Observational Consequences

Matias, CB

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- SLED predicts there are 6D massless fermions in

the bulk, as well as their properties - Massless, chiral, etc.
- Masses and mixings can be naturally achieved

which agree with data! - Sterile bounds oscillation experiments

Dimensionful coupling l 1/Mg

Observational Consequences

Matias, CB

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- SLED predicts there are 6D massless fermions in

the bulk, as well as their properties - Massless, chiral, etc.
- Masses and mixings can be naturally achieved

which agree with data! - Sterile bounds oscillation experiments

- SUSY keeps N massless in bulk
- Natural mixing with Goldstino on branes
- Chirality in extra dimensions provides natural L

Dimensionful coupling l 1/Mg

Observational Consequences

Matias, CB

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- SLED predicts there are 6D massless fermions in

the bulk, as well as their properties - Massless, chiral, etc.
- Masses and mixings can be naturally achieved

which agree with data! - Sterile bounds oscillation experiments

Dimensionful coupling! l 1/Mg

Observational Consequences

Matias, CB

t

Constrained by bounds on sterile neutrino emission

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- SLED predicts there are 6D massless fermions in

the bulk, as well as their properties - Massless, chiral, etc.
- Masses and mixings can be naturally achieved

which agree with data! - Sterile bounds oscillation experiments

Dimensionful coupling! l 1/Mg

Require observed masses and large mixing.

Observational Consequences

Matias, CB

t

Constrained by bounds on sterile neutrino emission

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- SLED predicts there are 6D massless fermions in

the bulk, as well as their properties - Massless, chiral, etc.
- Masses and mixings can be naturally achieved

which agree with data! - Sterile bounds oscillation experiments

- Bounds on sterile neutrinos easiest to satisfy if

g l v lt 10-4. - Degenerate perturbation theory implies massless

states strongly mix even if g is small. - This is a problem if there are massless KK modes.
- This is good for 3 observed flavours.
- Brane back-reaction can remove the KK zero mode

for fermions.

Dimensionful coupling! l 1/Mg

Require observed masses and large mixing.

Observational Consequences

Matias, CB

- Imagine lepton-breaking terms are suppressed.
- Possibly generated by loops in running to low

energies from Mg. - Acquire desired masses and mixings with a mild

hierarchy for g/g and e/e. - Build in approximate Le Lm Lt, and Z2

symmetries.

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- SLED predicts there are 6D massless fermions in

the bulk, as well as their properties - Massless, chiral, etc.
- Masses and mixings can be naturally achieved

which agree with data! - Sterile bounds oscillation experiments

S Mg r

Observational Consequences

Matias, CB

- 1 massless state
- 2 next- lightest states have strong overlap with

brane. - Inverted hierarchy.
- Massive KK states mix weakly.

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- SLED predicts there are 6D massless fermions in

the bulk, as well as their properties - Massless, chiral, etc.
- Masses and mixings can be naturally achieved

which agree with data! - Sterile bounds oscillation experiments

Observational Consequences

Matias, CB

Worrisome once we choose g 10-4, good masses

for the light states require e S k

1/g Must get this from a real compactification.

- 1 massless state
- 2 next- lightest states have strong overlap with

brane. - Inverted hierarchy.
- Massive KK states mix weakly.

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- SLED predicts there are 6D massless fermions in

the bulk, as well as their properties - Massless, chiral, etc.
- Masses and mixings can be naturally achieved

which agree with data! - Sterile bounds oscillation experiments

Observational Consequences

Matias, CB

- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics

- SLED predicts there are 6D massless fermions in

the bulk, as well as their properties - Massless, chiral, etc.
- Masses and mixings can be naturally achieved

which agree with data! - Sterile bounds oscillation experiments

2

- Lightest 3 states can have acceptable 3-flavour

mixings. - Active sterile mixings can satisfy incoherent

bounds provided g 10-4 or less (qi g/ci).

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