Understanding the Dark Understanding the Dark Energy From HolographyEnergy From Holography

Bin WangDepartment of Physics, Fudan University

Black Hole ThermodynamicsBlack Hole Thermodynamics

S=A/4S=A/4

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) 027503 )

E R

E R

+

))2/(1)(/( 2 ERehERS

hERSS BEB /

2/1222 ))/(1(/ REshERS

e

)]2/()/(1)[/( 22/1222 EReREshERS

“Entropy bounds for isolated system depend neither On background spacetime

nor on spacetime dimensions.”

Universal

The World as a HologramThe World as a HologramHolographic Principle

Entropy cannot exceed one unit per Planckian area of itsboundary surface

(Hooft, gr-qc/9310026; L. Susskind,J. Math. Phys. 36(1995)6337)

Holographic Entropy Bound (HEB)

2 pHEB AlSS

A Holographic SpacetimeA Holographic SpacetimeAdS/CFT Correspondence

“Real conceptual change in our thinking aboutGravity.”(Witten, Science 285(1999)512)

Comparison of BEB and HEBIsolated System

ForFor

Cosmological Consideration

22 2 2

/ / ( )

,,

BEB s p s

HEB p ps BEB HEBs BEB HEB

S ER GER G R Rl R GES Al R lR R S SR R S S

-- -

= = = == =

> <= =

h h

4 2 2 22

/ / / ( ) /( )BEB p p p p p

p FS HEB

S ER Md d Hd d lHd S

r-

= = = = =h h h

FS HEB BEBS S- <

Applying Holography in CosmologyApplying 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 density2) Cosmological constant3) new geometric structures of spacetimeWhat role can Holography play in studying DE? . .

Understanding DE by HolographyUnderstanding DE by Holography

Holographic constraint on a DE modelHolographic constraint on a DE modelB.Wang, E.Abdalla and R.K.Su, Phys.Lett. B611 (2005) 21 B.Wang, E.Abdalla and R.K.Su, Phys.Lett. B611 (2005) 21

Holographic Dark Energy ModelHolographic Dark Energy ModelMiao Li, Phys.Lett. B603 (2004) 1Miao Li, Phys.Lett. B603 (2004) 1, , JCAP 0408 (2004) 013 JCAP 0408 (2004) 013 Y.G.Gong, B. Wang and Y.Z.Zhang, hep-th/0412218 Y.G.Gong, B. Wang and Y.Z.Zhang, hep-th/0412218 B. Wang, Y.G.Gong and E. Abdalla, hep-th/0506069B. Wang, Y.G.Gong and E. Abdalla, hep-th/0506069

Holographic cosmic dualityHolographic cosmic dualityB.Wang et al Phys.Lett. B609 (2005) 200B.Wang et al Phys.Lett. B609 (2005) 200

B.Wang, E. Abdalla, hep-th/0501059B.Wang, E. Abdalla, hep-th/0501059

Holographic constraint on a DE modelHolographic constraint on a DE model

Model:Model:The effective low energy actionThe effective low energy action

Einstein equationEinstein equation

FRW ansatzFRW ansatz

Friedmann equationfor 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 It can be written as

wherewhere

Holographic constraint on a DE modelHolographic 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 modelHolographic 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 DEHolographic constraint on DEFor the cosmological setting, the particle hor

izon,

The ratio S/SB reads

1. S/SB<12. Physical particle horizon3. Accelerated expansion

Holographic constraint on DEHolographic constraint on DE

The future event horizon,

1. S/SB<12. Physical event horizon3. Accelerated expansion

Holographic constraint on DEHolographic constraint on DE

Holographic entropy boundHolographic entropy boundBoundary’s surface characterized by the

event horizon,

1. S/A<12. Physical event horizon3. Accelerated expansion

Holographic constraint on DEHolographic constraint on DE

Conclusion:Conclusion: Bekenstein bound and holographic bound Bekenstein bound and holographic bound

plays the same role here on DEplays the same role here on DE Constraints on DE has been givenConstraints on DE has been given Failure of using the particle horizon is that Failure of using the particle horizon is that

it refers to the early universeit refers to the early universe

Astro-ph/0404402Astro-ph/0404402

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

23pD LML D

2223 LMc pD

Interaction between DE/DMInteraction between DE/DM The total energy densityThe total energy density energy density of matter fieldsenergy density of matter fields dark energydark energy

conserved conserved [Pavon PRD(04)][Pavon PRD(04)]

Interaction between DE/DMInteraction between DE/DM Ratio of energy densities Ratio of energy densities

It changes with time.It changes with time. (EH better than the HH)(EH better than the HH)

Using Friedmann Eq, Using Friedmann Eq,

B. Wang, Y.G.Gong and E. Abdalla, hep-th/0506069

Evolution of the DEEvolution of the DEbigger, DE starts to play the role earlier, however at late stage, big DE approaches a small value

Evolution of the Evolution of the qq Deceleration AccelerationDeceleration Acceleration

Evolution of the equation of state of DEEvolution of the equation of state of DE

Crossing -1 behavior Crossing -1 behavior

Fitting to Golden SN dataFitting to Golden SN data

Results of fitting to golden SN data:Results of fitting to golden SN data:

If we set c=1, we haveIf we set c=1, we have

Our model is consistent with SN dataOur model is consistent with SN data

Dark Energy-----CMB Low Dark Energy-----CMB Low ll SuppressSuppress We will use coordinates for the metric of our universeWe 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 preferredA. Linde(JCAP03);Luminet(Nature03);Efstathiou(MNRAS03)

The spatial geometry of the universe was probed by supernova measurement of the cubic correctionto the luminosity distanceCaldwell astro-ph/0403003; B.Wang & Gong (PLB 605 (2005) 9

The Harmonic FunctionThe Harmonic FunctionThe harmonic function satisfies the generic Helmholtz equationThe harmonic function satisfies the generic Helmholtz equation

For the flat space, the above Eq. can be solved byFor 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 FunctionThe Harmonic FunctionWith our metric, the radial harmonic equation in the curved space is giveWith our metric, the radial harmonic equation in the curved space is give

n byn by

For the requirement that is single valued, satisfying the periodic

boundary condition

CMB power spectrum.

08.1,4 totcl

We cannot count on the intrinsic cutoff due to the curvature to explain the small l suppress of CMB

HOLOGRAPHIC UNDERSTANDING OF HOLOGRAPHIC UNDERSTANDING OF LOW-LOW-l l CMB FEATURECMB FEATURE

The relation between the short distance cut-off and the infraThe relation between the short distance cut-off and the infrared cut-offred cut-off

Translating the IR cutoff L into a cutoff at physical wavelengths

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)

Enqvist etal PRL(05); B.Wang et al PLB(05)

today

CMB/Dark Energy cosmic dualityCMB/Dark Energy cosmic dualityThus the relative position of the cutoff is the CMB spectrum Thus the relative position of the cutoff is the CMB spectrum

depends on the equation of state of dark energy.depends on the equation of state of dark energy.Given the experimental limits,Given the experimental limits,

Cutoff appears at l ~7

Holograpic constraint on the DEHolograpic 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 Holography can be a useful tool to understand dark tool to understand dark energyenergy

Thanks!Thanks!

IR cutoff = Event horizon?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.