1. Understanding the Dark Energy From Holography
Bin Wang
Department of Physics,
Fudan University

2. Black Hole Thermodynamics
S=A/4

3. Bekenstein Entropy Bound (BEB)
For Isolated Objects
Isolated physical system of energy and size (J.D. Bekenstein, PRD23(1981)287)
Charged system with energy , radius and charge (Bekenstein and Mayo, PRD61(2000)024022; S. Hod, PRD61(2000)024023; B. Linet, GRG31(1999)1609)
Rotating system (S. Hod, PRD61(2000)024012; B. Wang and E. Abdalla, PRD62(2000)044030)
Charged rotating system
(W. Qiu, B. Wang, R-K Su and E. Abdalla, PRD 64 (2001) ) +

4. nor on spacetime dimensions.”
“Entropy bounds for isolated system depend neither On background spacetime
nor on spacetime dimensions.”
Universal

5. The World as a Hologram Holographic Entropy Bound (HEB)
Holographic Principle
Entropy cannot exceed one unit per Planckian area of its
boundary surface
(Hooft, gr-qc/ ; L. Susskind, J. Math. Phys. 36(1995)6337)
Holographic Entropy Bound (HEB)

6. A Holographic Spacetime
AdS/CFT Correspondence
“Real conceptual change
in our thinking about
Gravity.”
(Witten, Science 285
(1999)512)

7. Comparison of BEB and HEB
Isolated System
For
Cosmological Consideration

8. Applying Holography in Cosmology
Holography implies a possible value of the cosmological constant in a large class of universes P. Horava and D. Minic, PPL. 85, 1610 (2000)
In an inhomogeneous cosmology it is a useful tool to select physically acceptable models
B. Wang, E. Abdalla and T. Osada, PRL 85 (2000) 5507
It can be used to study of inflation and gives possible upper limits to the number of e-folds
T. Banks and W. Fischler astro-ph/ ;
B. Wang and E. Abdalla, Phys.Rev. D69 (2004) ;
R. G. Cai, JACP 0402:007, 2004;

9. What is the Dark Energy? What role can Holography play in studying DE?
A surprising recent discovery has been the discovery that the expansion of the Universe is accelerating.
Implies the existence of dark energy that makes up 70% of the Universe
new, and often not well defined, components of the energy density
Cosmological constant
new geometric structures of spacetime
What role can Holography play in studying DE?
. .

10. Understanding DE by Holography
Holographic constraint on a DE model
B.Wang, E.Abdalla and R.K.Su, Phys.Lett. B611 (2005) 21
Holographic Dark Energy Model
Miao Li, Phys.Lett. B603 (2004) 1, JCAP 0408 (2004) 013
Y.G.Gong, B. Wang and Y.Z.Zhang, hep-th/
B. Wang, Y.G.Gong and E. Abdalla, hep-th/
Holographic cosmic duality
B.Wang et al Phys.Lett. B609 (2005) 200
B.Wang, E. Abdalla, hep-th/

11. Holographic constraint on a DE model
The effective low energy action
Einstein equation
FRW ansatz
Friedmann equation
for arbitrary 4-d brane-localized matter source
The feature persists for arbitrary number of dimensions.

12. Suppose that the effects of extra dimensions manifest themselves as a modification to the Friedmann equation
It can be written as
where

13. Holographic constraint on a DE model
The continuity equation still holds,
Thus
And
which can be written as [Eric. Linde(03)]

14. Holographic constraint on a DE model
Without dark energy, the universe expands as a~
Supposing now that the dark energy starts to play role, a~
To experience accelerated expansion,
which requires

15. Holographic constraint on DE
For the cosmological setting, the particle horizon,
The ratio S/SB reads
S/SB<1
Physical particle horizon
Accelerated expansion

16. Holographic constraint on DE
The future event horizon,
S/SB<1
Physical event horizon
Accelerated expansion

17. Holographic constraint on DE
Holographic entropy bound
Boundary’s surface characterized by the event horizon,
S/A<1
Physical event horizon
Accelerated expansion

18. Holographic constraint on DE
Conclusion:
Bekenstein bound and holographic bound plays the same role here on DE
Constraints on DE has been given
Failure of using the particle horizon is that it refers to the early universe

19. Astro-ph/

21. Holographic Dark Energy Model
QFT: Short distance cutoff
Long distance cutoff Cohen etal, PRL(99)
Due to the limit set by formation of a black hole
L – size of the current universe
-- quantum zero-point energy density
caused by a short distance cutoff
The largest allowed L to saturate this inequality is
L --- Future event horizon to
accommodate acceleration
Miao Li, PLB(04)

22. Interaction between DE/DM
The total energy density
energy density of matter fields
dark energy
conserved [Pavon PRD(04)]

23. Interaction between DE/DM
Ratio of energy densities
It changes with time. (EH better than the HH)
Using Friedmann Eq,
B. Wang, Y.G.Gong and E. Abdalla, hep-th/

24. Evolution of the DE
bigger, DE starts to play the role earlier, however at late stage, big DE approaches a small value

25. Evolution of the q
Deceleration Acceleration

26. Evolution of the equation of state of DE
Crossing -1 behavior

27. Fitting to Golden SN data
Results of fitting to golden SN data:
If we set c=1, we have
Our model is consistent with SN data

28. Dark Energy-----CMB Low l Suppress
We will use coordinates for the metric of our universe
The tendency of preferring closed universe appeared in a suite of CMB experiments
The improved precision from WMAP provides further confidence showing that a closed universe with positively curved space is marginally preferred
A. Linde(JCAP03);Luminet(Nature03);Efstathiou(MNRAS03)
The spatial geometry of the universe was probed by supernova measurement of the cubic correction
to the luminosity distance
Caldwell astro-ph/ ; B.Wang & Gong (PLB 605 (2005) 9

29. The Harmonic Function
The harmonic function satisfies the generic Helmholtz equation
For the flat space, the above Eq. can be solved by
Thus the purely spatial dependence of each mode of oscillation in spherical coordinates is represented in the form
For the nonzero curvature space, the only change in the metric is in the radial dependence, thus in the curved space

30. The Harmonic Function CMB power spectrum.
With our metric, the radial harmonic equation in the curved space is given by
For the requirement that
is single valued, satisfying the periodic
boundary condition
CMB power spectrum.
We cannot count on the intrinsic cutoff due to
the curvature to explain the small l suppress of CMB

31. HOLOGRAPHIC UNDERSTANDING OF LOW-l CMB FEATURE
The relation between the short distance cut-off and the infrared cut-off
Translating the IR cutoff L into a cutoff at physical wavelengths
today
Enqvist etal PRL(05);
B.Wang et al PLB(05)
we have the smallest wave number at present
The comoving distance to the last scattering follows from the definition of comoving time
f (z) relates to the equation of state of dark energy w(z)

32. CMB/Dark Energy cosmic duality
Thus the relative position of the cutoff is the CMB spectrum depends on the equation of state of dark energy.
Given the experimental limits,
Cutoff appears at
l ~7

33. Holograpic constraint on the DE
We concentrate on the static equation of state of dark energy here. From the WMAP data, the statistically significant suppression of the low multipole appears at the two first multipoles corresponding to l = 2; 3. Combining data from WMAP and other CMB experiments, the position of the cutoff lc in the multipole space falls in the interval 3 < lc < 7.

34. Holography can be a useful tool to understand dark energy
Thanks!

35. IR cutoff = Event horizon?
L=event horizon and considering the suppression position within the interval 3 < lc < 7,
This shows that even if an IR/UV duality is at work in the theory at some fundamental level, the IR regulator might not be simply related to the future event horizon.
There might still be a complicated relation between the dark energy and the IR cutoff the CMB perturbation modes.
To get the firm answer, the exact location of the suppression point and the precise shape of the CMB spectrum are crucial.