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

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

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

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

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

Stability Conditions Eigenvalues of the matrix M Stability Conditions

Scalar field with exponential potential

Autonomous System Define

Fixed points and attractors PRD 57 (1998）4686

Interacting Models arXiv: 0811.1698, 0812.1117

Fixed points Fixed points Stability conditions for fixed point 4

Stability arXiv: 0811.1698 PRD 78 (2008) 023505

Phase diagram for fixed point 4

Phase diagram 1

Interacting model 2 Model 2:

Stability Condition For fixed point 4

Stability condition

Properties of fixed points

Interacting Model 3 Model 3:

Stability Condition Point 4: Point 5:

Stability Conditions cont

Phase diagram

Interacting Phantom Models

Model 1 Model 1

Stability Condition

Phase diagram

Interacting model 2 Model 2:

Interacting model 3 Model 3:

Interacting model 4 Model 4:

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

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