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 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 ) +

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

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/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 For Cosmological Consideration

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? 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? . .

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 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 S/SB<1 Physical particle horizon Accelerated expansion

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

Holographic constraint on DE Holographic entropy bound Boundary’s surface characterized by the event horizon, 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 -- 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)

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 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

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)

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.