1. Coincidence Problem in Interacting Dark energy model
Yungui Gong (龚云贵)
Chongqing University of Posts and Telecommunications
重庆邮电大学数理学院
December 9, 2008, IHEP Cosmology Workshop

2. Outlines Coincidence problem Phase-space Analysis
Attractors in scalar field with exponential potential
Interacting Models
Interacting Phantom Models
Summary

3. Coincidence Problem Why now
It does not depend on the initial conditions
Attractor Solutions： the system settles into the state no matter what the initial conditions are

4. Autonomous System Autonomous system Fixed points:
Stability against small perturbations?

5. Stability Perturbation around the fixed points
To the first order of perturbation

6. Stability Conditions
Eigenvalues of the matrix M
Stability Conditions

7. Scalar field with exponential potential

8. Autonomous System
Define

9. Fixed points and attractors
PRD 57 (1998）4686

10. Interacting Models
arXiv: ,

11. Fixed points
Fixed points
Stability conditions for fixed point 4

12. Stability
arXiv:
PRD 78 (2008)

13. Phase diagram for fixed point 4

14. Phase diagram 1

15. Interacting model 2
Model 2:

16. Stability Condition
For fixed point 4

17. Stability condition

18. Properties of fixed points

19. Interacting Model 3
Model 3:

20. Stability Condition
Point 4:
Point 5:

21. Stability Conditions cont

22. Phase diagram

23. Interacting Phantom Models

24. Model 1
Model 1

25. Stability Condition

26. Phase diagram

27. Interacting model 2
Model 2:

28. Interacting model 3
Model 3:

29. Interacting model 4
Model 4:

30. Summary
Interacting Quintessence models may alleviate the coincidence problem
Interacting Phantom models are not good to solve the coincidence problem

31. Thank You!