Cosmological Constant as a Manifestation of the Hierarchy

1
Cosmological Constant as a Manifestation of the
Hierarchy
Pisin Chen Leung Center for Cosmology and
Particle Astrophysics National Taiwan
University Kavli Institute for Particle
Astrophysics and Cosmology Stanford University
PC, Nucl. Phys. Proc. Suppl.173, 137 (2007). PC
and J-A. Gu, Mod. Phys. Lett. A22, 1995 (2007)
arXiv0712.2441

• 3rd Biennial Leopoldina Conference on Dark
  Energy, Munich, Oct. 7-11, 2008

2
Where we Stand now
SN Ia (SNLS, Higher-Z, Essence, low-Z stuff)
WMAP5 BAO(SDSS) HST H0
Brian Schmidts talk
If it looks like an apple and tastes like an
apple, then it must be an apple!
- PC
Kowalski et al 08
?w ?? 1
3
Smallness of Dark Energy

• Combination of recent data from WMAP3 SDSS
• determines w - 0.94 0.09
• for dark energy (DE) equation of state p
  w?.
• SNLS gives w -1.023 0.090 (stat)
  0.54(sys).

DE likely a bone fide CC w - 1.
If DE never changes in space and time, then it
must be associated with fundamental properties
of spacetime.

• Observations

Why much smaller than standard model scale?

?DE1/4
10-15 !
MSM
4
Another Hierarchy in Physics

• Gravity is much weaker, or Planck scale (1019
  GeV),
• much larger, than that of SM gauge
  interactions
• MPl
• MSM

1016 .
Two well-known solutions ADD large (but flat)
extra dimensions RS warped geometry in x-d
5
A Numerical Coincidence

• A remarkable numerical coincidence,
• Perhaps not accidental but implies a deeper
  connection
• Caution Unlike the 1st hierarchy that links 4
  fundamental interaction strengths, DE must be a
  secondary, derived quantity.

6
Analogy in Atomic Physics

• Bohr atom
• Fundamental energy scale in Schrödinger equation
  me
• Ground state energy suppressed by 2 powers of
  fine structure constant

• Dark energy
• Fundamental energy scale in quantum gravity MPl
• Dark energy suppressed by 2 powers of gravity
  fine structure constant

7
Gravity lives in the bulk while gauge
interactions live on the brane.
dxµ
dx?

Visible brane
Hidden brane
Y0
Yp
8
Casimir Effect
QED vacuum fluctuations
9
Casimir Energy
?casimir ?vac ( ) ? ?vac(a ? ?) 8 a-4
a
(a ? ?)
10
Casimir Energy vs. Vacuum Energy

• Casimir energy px ??, py gt 0.
• py cannot be tuned away.
• Conventional vacuum energy (brane tension)
• px ??, py 0.
• py can in principle be tuned away.

px

py
11
Strategy for the Smallness of Dark Energy
Brane World
Supersymmetry

?vac(4) (mn - mn-1)2 ?mn2
12

• By definition, the Casimir energy under SUSY
  breaking is
• which is
• The KK mass shift can be shown to scale as
• The SUSY-KK graviton/gravitino energy spectrum,
  on the other hand, goes like

13
Casimir Energy under SUSY-Breaking
Putting all these together, we find


14
Summary

• Dark energy may very well be a cosmological
• constant.
• The numerical coincidence between the SM-Planck
• and the SM-DE hierarchies suggests a deeper
• connection between the two.
• This approach does not attempt to solve the
  old
• CC problem, i.e., the problem of 10120.
  Assuming
• that this old CC problem will be resovled
  someday,
• our model seems able to solve the new CC
• problem, i.e., the smallness of CC as inferred
  by
• observations.