Transcript Understanding the Dark Energy From Holography Bin Wang Department of Physics,

Understanding the Dark Energy
From Holography
Bin Wang
Department of Physics,
Fudan University
Black Hole Thermodynamics
S=A/4
Bekenstein Entropy Bound (BEB)
For Isolated Objects


Isolated physical system of energyE and size R
S  S BEB  ER / h
(J.D. Bekenstein, PRD23(1981)287)
Charged system with energy E , radius R and charge
S  ( ER / h)(1  e 2 /( 2 ER))
e
(Bekenstein and Mayo, PRD61(2000)024022; S. Hod,
PRD61(2000)024023; B. Linet, GRG31(1999)1609)

Rotating system
S  ER / h(1  s 2 /( E 2 R 2 ))1/ 2
(S. Hod, PRD61(2000)024012; B. Wang and E. Abdalla, PRD62(2000)044030)
•
Charged rotating system
S  ( ER / h)[1  s 2 /( E 2 R 2 )1/ 2  e2 /( 2ER)]
(W. Qiu, B. Wang, R-K Su and E. Abdalla, PRD 64 (2001) 027503 )
+
“Entropy bounds for isolated system depend
neither On background spacetime
nor on spacetime dimensions.”
Universal
The World as a Hologram
Holographic Principle
Entropy cannot exceed one unit per Planckian area of its
boundary surface
S  S HEB  Al
2
p
(Hooft, gr-qc/9310026; L. Susskind,
J. Math. Phys. 36(1995)6337)
Holographic Entropy Bound (HEB)
A Holographic Spacetime
AdS/CFT Correspondence
“Real conceptual change
in our thinking about
Gravity.”
(Witten, Science 285
(1999)512)
Comparison of BEB and HEB
Isolated System
S BEB = ER / h = GER / (G h ) = R s R lp- 2 R s = GE
S HEB = A lp- 2 = R 2lp- 2
For R > R s , S BEB < S HEB
For R = R s , S BEB = S HEB
Cosmological Consideration
S BEB = ER / h = Md p / h = r d p4 / h = (Hd p )2 d p2 / lp2 =
(Hd p )2 S FS - HEB
S FS - HEB < S BEB
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/0307459;
B. Wang and E. Abdalla, Phys.Rev. D69 (2004) 104014;
R. G. Cai, JACP 0402:007, 2004;
What is the Dark Energy?
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
1) new, and often not well defined, components of the
energy density
2) Cosmological constant
3) new geometric structures of spacetime
What role can Holography play in
studying DE?
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/0412218
B. Wang, Y.G.Gong and E. Abdalla, hep-th/0506069
 Holographic
cosmic duality
B.Wang et al Phys.Lett. B609 (2005) 200
B.Wang, E. Abdalla, hep-th/0501059
Holographic constraint on a DE model
 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.
Suppose that the effects of extra dimensions
manifest themselves as a modification to
the Friedmann equation
It can be written as
where
Holographic constraint on a DE model
The continuity equation still holds,
Thus
And
which can be written as [Eric. Linde(03)]
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
Holographic constraint on DE
For the cosmological setting, the particle
horizon,
The ratio S/SB reads
1.
2.
3.
S/SB<1
Physical particle horizon
Accelerated expansion
Holographic constraint on DE
The future event horizon,
1.
2.
3.
S/SB<1
Physical event horizon
Accelerated expansion
Holographic constraint on DE
Holographic entropy bound
Boundary’s surface characterized by the
event horizon,

1.
2.
3.
S/A<1
Physical event horizon
Accelerated expansion
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
Astro-ph/0404402
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
3
 D L  LM p  D -- 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
2
2 2
accommodate acceleration
2
 D  3c M p L
Miao Li, PLB(04)
Interaction between DE/DM


The total energy density
energy density of matter fields
dark energy
conserved
[Pavon PRD(04)]
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/0506069
Evolution of the DE
bigger, DE starts to play the role earlier,
however at late stage, big
DE approaches
a small value
Evolution of the q

Deceleration
Acceleration
Evolution of the equation of state of DE

Crossing -1 behavior
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
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/0403003; B.Wang & Gong (PLB 605 (2005) 9
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
The Harmonic Function
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.
lc  4, tot  1.08
We cannot count on the intrinsic cutoff due to
the curvature to explain the small l suppress of CMB
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
Enqvist etal PRL(05);
B.Wang et al PLB(05)
today
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)
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
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.
Holography can be a useful
tool to understand dark
energy
Thanks!
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.