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On the degeneracy between w 0 and w a

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

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On the degeneracy between w 0 and w a

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  1. On the degeneracy between w0 and wa Yungui Gong Huazhong Univ of Science and Tech 华中科技大学 龚云贵 The 7th Aegean Summer School, Paros, Greece, 2013.9.27

  2. Contents • Motivations: General Property of Scalar Field dynamics • Dark energy parametrizations • The degeneracy between w0 and wa • 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 • w0 and wa 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 • 0th 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 w0 and wa • The reduced degeneracy helps improve the constraint on w(z)

  25. THANK YOU！

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