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Cosmological Constant as a Manifestation of

the HierarchyPisin Chen

Leung Center for Cosmology and Particle AstrophysicsNational Taiwan University

&Kavli Institute for Particle Astrophysics and Cosmology

Stanford University

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

PC, Nucl. Phys. Proc. Suppl.173, 137 (2007).PC and J-A. Gu, Mod. Phys. Lett. A22, 1995 (2007); arXiv:0712.2441

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SN Ia (SNLS, Higher-Z, Essence, low-Z stuff) + WMAP5 +BAO(SDSS)+ HST H0

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Kowalski et al 08

w+=1

Where we Stand now

Brian Schmidt’s talk

If it looks like an apple and tastes like an apple, then it must be an apple! - PC

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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 = wρ. • SNLS gives w = −1.023 ± 0.090 (stat) ± 0.54(sys).

Why much smaller than standard model scale?

DE likely a bone fide CC: w = − 1.

• Observations

~ 10-15 !ρDE

1/4

MSM

If DE never changes in space and time, then it must be associated with fundamental properties of spacetime.

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Another Hierarchy in Physics

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

MPl

MSM

Two well-known solutions:ADD : large (but flat) extra dimensions RS : warped geometry in x-d

~ 1016 .

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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.

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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”

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Randall-Sundrum Warped Geometry

Y=0Y=π

Visible brane Hidden brane

dxμdxν

Gravity lives in the bulk while gauge interactions live on the brane.

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Casimir Effect

QED vacuum fluctuations

9(a ) a

Casimir Energy

casimir = vac (| |) vac(a ) ∞ a-4

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Casimir Energy vs. Vacuum Energy

py

px

• Casimir energy: px = ‒ρ, py > 0. py cannot be tuned away.• Conventional vacuum energy (brane tension): px = ‒ρ, py = 0. py can in principle be tuned away.

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Strategy for the Smallness of Dark Energy

Supersymmetry Brane World

BUT SUSY only on the brane

= 0vac:boson fermion

+

vac(4)

~ (mn - mn-1)2 mn

2

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• 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

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Casimir Energy under SUSY-Breaking

Putting all these together, we find

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.