Title: The Cosmological Constant on the Brane
1The Cosmological Constant on the Brane
- New Approaches
- to Naturalness
- Cliff Burgess
2Partners 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
3The 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 Newtons Law Neutrino
Oscillations
4Naturalness and Dark Energy
- Why doesnt the electron contribute too large a
zero-point energy to the cosmological constant?
5Technical Naturalness
- This may have to wait until we know the
fundamental theory. - This is serious because it involves physics we
think we understand
- Given a small quantity l l0 dl
- In the fundamental theory, why should l0 be
small? - Given that l0 is small, why does it stay small as
one integrates out physics up to the scales for
which l is measured?
6Anthropism v. Technical Naturalness
- Given a small quantity l l0 dl
- Why cant l0 cancel dl?
- Given enough vacua perhaps this cancellation
occurs in some. - It may only be possible to discuss this problem
in those vacua where cancellation occurs.
7Anthropism v. Technical Naturalness
- Possibly, but
- Other hierarchies have natural understanding
- Leads one to stop thinking about how to solve the
problem. - Perhaps the 6D case to be presented is more
likely than the 4D fine-tuned solution.
- Given a small quantity l l0 dl
- Why cant l0 cancel dl?
- Given enough vacua perhaps this cancellation
occurs in some. - It may only be possible to discuss this problem
in those vacua where cancellation occurs.
8Scales
How can these scales be changed to reduce the
vacuum energys gravity?
These scales are natural using standard 4D
arguments.
9Vacuum Energy 4D Curvature
Arkani-Hamad et al Kachru et al, Carroll
Guica Aghababaie, et al
- 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.
10The SLED Proposal
- Suppose physics is extra-dimensional above the
10-2 eV scale. - Suppose the physics of the bulk is supersymmetric.
11The SLED Proposal
- Suppose physics is extra-dimensional above the
10-2 eV scale. - Suppose the physics of the bulk is supersymmetric.
- Experimentally possible
- There are precisely two extra dimensions at these
scales - We are brane bound
12The SLED Proposal
- Suppose physics is extra-dimensional above the
10-2 eV scale. - Suppose the physics of the bulk is supersymmetric.
- Experimentally possible
- There are precisely two extra dimensions at these
scales - We are brane bound
- The 6D gravity scale is in the TeV region.
13The SLED Proposal
- Suppose physics is extra-dimensional above the
10-2 eV scale. - Suppose the physics of the bulk is supersymmetric.
- Experimentally possible provided
- SUSY breaks at scale Mg on the branes
- Trickle-down of SUSY breaking to the bulk is
14Scales
Naturalness for these scales must be rethought in
6D.
These scales are natural using standard 4D
arguments.
15The CC Problem in 6D
- The 6D CC
- Integrate out brane physics
- Integrate out bulk physics
- Classical contribution
- Quantum corrections
16The CC Problem in 6D
- The 6D CC
- Integrate out brane physics
- Integrate out bulk physics
- Classical contribution
- Quantum corrections
- Several 6D SUGRAs are known, including chiral and
non-chiral variants. - None have a 6D CC.
17The CC Problem in 6D
Nishino Sezgin
- The 6D CC
- Integrate out brane physics
- Integrate out bulk physics
- Classical contribution
- Quantum corrections
- Several 6D SUGRAs are known, including chiral and
non-chiral variants. - None have a 6D CC.
18The CC Problem in 6D
- The 6D CC
- Integrate out brane physics
- Integrate out bulk physics
- Classical contribution
- Quantum corrections
- Generates large 4D vacuum energy
- This energy is localized in the extra dimensions
(plus higher-derivatives)
19The CC Problem in 6D
- The 6D CC
- Integrate out brane physics
- Integrate out bulk physics
- Classical contribution
- Quantum corrections
- Solve classical equations in presence of branes
- Plug back into action
20The CC Problem in 6D
Chen, Luty Ponton
- The 6D CC
- Integrate out brane physics
- Integrate out bulk physics
- Classical contribution
- Quantum corrections
- Solve classical equations in presence of branes
- Plug back into action
Tensions cancel between brane and bulk!!
21The CC Problem in 6D
Aghababaie et al.
- The 6D CC
- Integrate out brane physics
- Integrate out bulk physics
- Classical contribution
- Quantum corrections
- Solve classical equations in presence of branes
- Plug back into action
Smooth parts also cancel for supersymmetric
theories!!
22The CC Problem in 6D
- The 6D CC
- Integrate out brane physics
- Integrate out bulk physics
- Classical contribution
- Quantum corrections
- Bulk is a supersymmetric theory with msb 10-2
eV - Quantum corrections can be right size in absence
of msb2 Mg2 terms! - Lifts flat direction.
23What 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?
24What 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?
25What 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 kind of bulk geometry arises from a given
pair of branes?
266D 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
276D 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
286D Solutions No Branes
- Why a flat solution?
- 80s Unit magnetic flux leaves SUSY
- unbroken
-
296D 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!
306D 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
316D Solutions Conical Singularities
Gibbons, Guven Pope Aghababaie, CB, Cline,
Firouzjahi, Parameswaran, Quevedo Tasinato
Zavala
- General solutions with two conical
singularities - Unequal conical defects lead to warped
geometries in the bulk - All such (static) solutions have flat 4D
geometries
326D 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
336D 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
346D 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
356D 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
366D Solutions Time-dependence
Tolley, CB, de Rham Hoover
- 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 - Nonlinear Plane-Wave Solutions
- Describe eg passage of bubble-nucleation
wall along the brane
376D 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.
38What 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?
- 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.
39What About Weinbergs Theorem?
- Weinberg has a general objection to self-tuning
mechanisms for solving the cosmological constant
problem.
40What About Weinbergs Theorem?
- Weinberg has a general objection to self-tuning
mechanisms for solving the cosmological constant
problem.
41What About Weinbergs Theorem?
- Weinberg has a general objection to self-tuning
mechanisms for solving the cosmological constant
problem.
42What About Weinbergs Theorem?
- Weinberg has a general objection to self-tuning
mechanisms for solving the cosmological constant
problem.
43Observational Consequences
- Quintessence cosmology
- Modifications to gravity
- Collider physics
- Neutrino physics
- Astrophysics
44Observational 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
45Observational 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
46Observational 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
47Observational 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
Radiation Matter Total Scalar w Parameter
w 0.9
48Observational 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
49Observational 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
50Observational 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.
51Observational 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.
52Observational 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
53Observational 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
54Observational 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
55Observational 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
56Observational 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
57Observational Consequences
Matias, CB London
- 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.
58Observational Consequences
Matias, CB London
- 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
59Observational Consequences
Matias, CB London
- 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
60Observational Consequences
Matias, CB London
- 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
61Observational Consequences
Matias, CB London
- 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
62Observational Consequences
Matias, CB London
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.
63Observational Consequences
Matias, CB London
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 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.
64Observational Consequences
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 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
65Observational Consequences
Matias, CB London
- 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
66Observational Consequences
Matias, CB London
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
67Observational Consequences
Matias, CB London
- 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).
68Observational 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
69The Good News
- Technically natural solution to the cosmological
constant problem may be possible. - Unconventional realization of weak-scale
supersymmetry breaking. - Enormously predictive, with many observational
consequences. - Cosmology at Colliders! Tests of gravity
70Current 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?