1 / 20

Dark Energy as a Manifestation of the Hierarchy

Dark Energy as a Manifestation of the Hierarchy. Joint Davis-NTU Workshop, December 15-18, 2008. Pisin Chen Department of Physics & Graduate Institute of Astrophysics & Leung Center for Cosmology and Particle Astrophysics National Taiwan University.

abrego
Download Presentation

Dark Energy as a Manifestation of the Hierarchy

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Dark Energy as a Manifestation of the Hierarchy Joint Davis-NTU Workshop, December 15-18, 2008 Pisin Chen Department of Physics & Graduate Institute of Astrophysics & Leung Center for Cosmology and Particle Astrophysics National Taiwan 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. Randall-Sundrum Warped Geometry Weakness of gravity = smallness of graviton wave function at visible brane dxμ dxν Hidden brane Visible brane MPl ~ 1016TeV MSM~TeV MSM = e-πka MPl ~ 10-16 k~MPl , e-kay Y=π Y=0

  9. Casimir Effect QED vacuum fluctuations

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

  11. 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

  12. 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

  13. Casimir Energy in RS Geometry • Consider the following action in 5-d action • (Gherghatta & Pomarol, 2001, 2002): • where • Here is the anti- symmetric product of gamma matrices,

  14. Casimir Energy in RS Geometry • The gravitino SUSY transformation is given by • From the action, the bulk gravitino satisfies the 5D • Schwinger-Rarita equation in the AdS background, • Assume separation of variables, we KK-decompose • the 5D gravitino field as • where are defined as even (odd) under • Z2 parity.

  15. SUSY Solution • Solving the equation of motion, it can be shown that • (Gherghatta-Pomarol, 2001) the y-dependent gravitino • wavefunctions are • Jμ, Yμ= Bessel functions and • satisfies the boundary condition • Solving this equation, one finds the 4D KK gravitino mass as

  16. SUSY-Breaking by Higgs on the Brane • Now we invoke Higgs coupling to the gravitino on the TeV brane: • where is the Higgs field and f(n)= f(n)L+ f(n)R.

  17. It can be shown thatthis will induce a KK gravitino mass-shift for the nth mode • Graviton, on the other hand, remains massless (at tree-level).

  18. 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

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

  20. 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, that is, the problem of 10120 (~Mpl4). • Assuming that this old CC problem will be resolved • someday, our model seems able to solve the “new” • CC problem, i.e., the smallness of CC as inferred • by observations.

More Related