1. On the degeneracy between w 0 and w a Yungui Gong Huazhong Univ of Science and Tech 华中科技大学 龚云贵 The 7 th Aegean Summer School, Paros, Greece, 2013.9.27

2. Contents  Motivations: General Property of Scalar Field dynamics  Dark energy parametrizations  The degeneracy between w 0 and w a  The consequence of the derived degeneracy

3. Motivations  General Property of scalar field dynamics  scalar field as dark energy: Tracking solutions  Tracker fields (Steinhardt etal, PRD 1999)

4. Tracking Solutions

5. Tracking Solution: General Property  Almost independent of initial conditions  Relation  Common Dynamics for scalar fields

6. Efstathiou Parametrization  Dark energy parametrization: capture the main dynamics of scalar field MNRAS 383, 879 (1999)

7. CPL Parametrization  Approximation E. Linder astro-ph/0210217

8. The degeneracy in CPL model  w 0 and w a is degenerated  What is the degeneracy? related with ?

9. Dark Energy Parametrizations (Partial Lists)  Dark energy parametrization: capture the main dynamics of scalar field  Efstathiou 1999, MNRAS 310, 842  CPL, Chevallier & Polarski 2001, IJMPD 10, 213; Linder 2003, PRL 90, 091301  JBP, Jassal, Bagla & Padmanabhan, MNRAS 356, L11  Wetterich 2004, PLB 594, 17

10. Scalar Field approximation  Cosmological equations

11. Scalar Field Dynamics  Take the (Slow-roll) approximation  For Thawing scalar field Scherrer & Sen 2008, PRD 77, 083515

12. approximation

13. Thawing scalar fields  Approximate w(z) dotted curve short dash curve long dash curve

14. The degeneracy between and  Relation  0 th order approximation Scherrer and Sen 2008, PRD 78, 067303

15. SSLCPL model  Taylor Expansion Gong etal., Int. J. Mod. Phys. 22 (2013) 1350035, 1301.1224

16. The accuracy of the approximation

17. SSWCPL model  Take approximation

18. The accuracy of the approximation

19. The degeneracy  Self-consistency

20. Flat SSLCPL Results

21. Flat SSWCPL Results

22. Flat CPL Results

23. Comparisons

24. Conclusions  The dynamics of scalar fields has some common features  The exists an approximate relation between w and  For thawing models, the dynamics can be approximated by CPL parametrization with degenerated relation between w 0 and w a  The reduced degeneracy helps improve the constraint on w(z)

25. THANK YOU ！