Causality Problem in Holographic Dark Energy Hyeong-Chan Kim Korea National University of Transportation, with Jungjai Lee (Daejin U.) and Jae-Weon Lee (Jungwon U.) 15 June 2012, Haeundae, Pusan 2012 international workshop for string theory and cosmology

Dark energy Holographic dark energy Einstein equation with HDE Causality problem and Circulation of logic problem Future Event Horizon  Future acceleration? Causality violation? Circulation of Logic problem? Summary

Accelerating expansion Inflation Decelerating expansion Inflection time History of the Universe Fine tuning? Coincidence Coincidence?

Eq. of state Energy budget of the universe Metric: Einstein Eq: Equation of state:

Modified gravity Quintessence K-essence Chaplygin gas Phantom (w<-1) Braneworld Backreaction Cosmic string Vac. Energy Quantum fluctuation Surface tension Holographic dark energy Dark energy from future event horizon (M. Li, 04) Dark energy from quantum energy fluctuations (Padamanabhan06) Agegraphic dark energy model (Cai07,Myung07) Dark energy from cosmic Hawking radiation (Kim,Lee,Lee08) Dark energy from Ricci scalar curvature (Gao,Wu,Chen,Shen,09)... Dark Energy Models

Black Holes and Entropy Black holes are “maximal entropy objects” Entropy of a black hole proportional to surface area of event horizon [G. t’Hooft, Susskind]. Max entropy for volume of space will be bounded by the surface area, not mass or volume

The Holographic Principle All information about a physical system in some region of space is encoded in its boundary surface, not its volume

How many degrees of freedom do I have? Marionette The Marionette How many degrees of freedom does this marionette have?

What is the maximum number of ropes he can have? The number of ropes should be given by the area of the sphere divided by the inverse of the UV cutoff scale^2. In this sense, the maximal entropy of a system in a volume may be proportional to its surface area. DOF of the Marionette

Holographic Cosmology Space-time and everything in it emerges dynamically out of the interaction of the particles living on the boundary Photo Credit & Copyright: Jason Ware

t Event horizon and particle horizon But who knows the end of the universe??? ?,

Event horizon in Penrose Diagram The horizon is a boundary surface such that any light departing from outside the surface cannot arrive the origin however time past.

Holographic dark energy from quantum entanglement 1 st law of thermodynamics Hawking temperature Energy related to the horizon Spin degree of freedom for massless scalar [Q]Find the energy density: Lee, Lee,Kim07

Note that the distance to the horizon appears to be explicitly dependent on the future evolution of the scale factor. Einstein equation including HDE Energy density of the holographic dark energy(HDE) Energy density other than the HDE Hubble parameter Portion of the HDE

Acausality and Circulation of Logic Acausality: –If a lucky guy modifies the future event horizon (FEH) in the future, it may affect the present motion of the universe. –Then, can we predict the next moment of the universe from the present data in the absence of the future knowledge? Circulation of Logic: –We do not know whether the universe will accelerates or not in the future. –In the presence of HDE, the universe is destined to expand with accelerating rates. –Then, can we use the FEH even if we do not know its presence? –Other horizons than FEH do not accelerates the universe.

Insight from M. Li 04 Introduce conformal time: –Comoving time is not good to understand the causal structure. –The metric: –The formula to the horizon distance appears to be causal now (no integration and no dependence on the future). How about for general cases? Is this philosophically satisfactory?

Does the FEH in EOM always leads to future acceleration? Consider an energy density: And watch whether it accelerates the universe or not. Consider the case No future acceleration in this case. This nullify the assumption! Equation of motion: Solution:

Questions on Causality violation Assume that a lucky guy succeed to change the FEH at present unexpectedly in a future. (even though it is impossible by definition) Q1 : Does this not modify the present evolution of the universe? Q2: Does this imply the causality violation for us at present? In other word, can we notice it? For the question I, we should say “yes” since the equation of motion explicitly depends on the future.

Examine the evolution equation in detail: Separate integration: Separate acausal part: Remove by differentiating once: We have obtained a causal second order evolution equation. Causal and Acausal part of the evolution equation

The acausal part does not affect on the evolution eq. –We do not need future information any more. – can be determined from the initial data and evolution equation. is not always well-defined. –Well defined only if: –Even if is ill-defined, the evolution equation works well. from the initial condition: –In this sense, does the role of boundary condition rather than a future dependent constant.

Causality violation problem Causality violation: It happens something unexpected from the past data at present. With this definition of causality, There is no causality violation for us in the universe with HDE. Even if some lucky guy succeed to change the FEH, he only change, (the initial condition) and the universe evolves with the well posed evolution equation. Therefore, he cannot notice the fact that the universe is modified.

Circulation of Logic problem Cosmological EH cannot be created or be annihilated by any classical mean. –The cosmological sol are divided into two classes: with horizon, without horizon. Can we find out where we are living of the two classes?  In principle “yes” without future information if we can solve the evolution equation. –Assumption for the homogeneity of space is crucial. –Still, we cannot say where we are living of the two until we get precise present data. –However, the use of the EOM can be justified.

Summary and Discussions Briefly introduced the HDE Einstein equation with HDE  well posed evolution equation + acausal constant The acausal part does the role of initial condition and may not give c ausality violation for appropriate definition of causality. We also discussed about the circulation of logic problem. It is still puzzling why HED ~time dependent horizon size.

Thank you for Listening!