Cosmological Constant as a Manifestation of the Hierarchy

1. Cosmological Constant as a Manifestation of the Hierarchy 3rd Biennial Leopoldina Conference on Dark Energy, Munich, Oct. 7-11, 2008 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); arXiv:0712.2441

2. Where we Stand now SN Ia (SNLS, Higher-Z, Essence, low-Z stuff) + WMAP5 +BAO(SDSS)+ HST H0 Brian Schmidt’s 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 = wρ. • 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? ρDE1/4 ~ 10-15! MSM

4. Another Hierarchy in Physics • Gravityis 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. 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” Analogy in Atomic Physics

7. Randall-Sundrum Warped Geometry Gravity lives in the bulk while gauge interactions live on the brane. dxν dxμ Visible brane Hidden brane Y=π Y=0

8. Casimir Effect QED vacuum fluctuations

9. Casimir Energy casimir = vac (||) vac(a  ) ∞ a-4 a (a  )

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

11. Strategy for the Smallness of Dark Energy = 0 + vac: fermion boson only on the brane BUT SUSY 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.