Kyung Yee Kim, Hyung Won Lee and Yun Soo Myung

1. Dark energy – microscopic understanding Kyung Yee Kim, Hyung Won Lee and Yun Soo Myung Relativity research center and School of Computer Aided Science Inje University

2. 1. introduction • The present Universe : • accelerated expansion supernova type Ia (SN Ia) data • negative pressure cosmological constant, dark energy, quintessence, k- essence , holographic dark energy, phantom matter… • Different context which negative pressure occur in: • Quantum processes in the early universe may phenomenologically be equivalent to effective negative bulk pressure. • For gaseous matter with specific internal self-interaction, negative bulk pressures can be derived within the frame work of relativistic gas dynamics. Drive accelerated expansion of universe

3. I. Two fluid model - macroscopic • Exist Interaction between form of matter for cosmological constant and dark matters • Macroscopic two fluid model • energy transfer between two matters II. Self-interacting gas model - microscopic In order to understanding between two matters, we introduce self-interacting gas model. Interaction between gases indicates microscopic antifrictional force coefficients

4. The FRW metric: • The first Friedmann equation: • The continuity equation :

5. 2. Two fluid model • Interacting model • continuity equation

6. continuity equation with • two continuity equation  two dissipative imperfect fluid

7. effective equation of state • Second Fridmann equation • Two density parameters

8. Holographic energy density with the future event horizon • A form of holographic energy density • Future event horizon  In order to study a variable of two energy densities • Considering the definition of holographic energy density

9. Holographic energy equation of state with • A form of differential equation For r = const, For r = variable,

10. n=1, c=1.0 case:

11. n=1/2, c=1.0 case:

12. n=0 , c=1.0 case:

13. n=0 , c=1.0 case:

14. self-interacting gas Drive accelerated expansion of universe. Interaction = effective one-particle forces. These forces act like friction or antifriction. • Pressure appears as the result of effective one particle force of form . • The equation of motion for gas particles moving under the influence of a force field. • Effective one particle force : depends on the Hubble rate. relates to the Ricci scalar. describes an interaction of individual particle with a space- time curvature. 3. Self-interacting gas model

15. The effective one-particle force : cosmological dynamics Homogeneous and isotropic models require a geodesic mean motion, but not necessarily a geodesic motion of the individual particles. The difference between macroscopic four-velocity and particle velocity give rise to make the effective one-particle force . So, a force makes the individual particles move in non-geodesic trajectories, while the macroscopic mean motion remains geodesic. A deviation from the geodesic motion of microscopic constituents due to a force may result in an effective negative pressure of the cosmic medium.

16. A gas dynamic of perfect fluid that consists of particles with mass, : geodesics trajectory • A gas dynamic of imperfect fluid that moves under the influence of a force field : non- geodesics trajectory

17. An interaction term in the Boltzmann equation gives rise to source the balance equation. . • Boltzmann equation: the one-particle distribution function . • The corresponding equilibrium distribution function: • The continuity equation:

18. Macroscopically , the action of force manifests itself as dissipative pressure. • Connection between equation of state and effective one-particle force:

19. Solution • The connection between force and Ricci scalar : • The state equation: • A single evolution equation:

21. 4. Result