On the degeneracy between w 0 and w a
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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

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


Contents

Contents

  • Motivations: General Property of Scalar Field dynamics

  • Dark energy parametrizations

  • The degeneracy between w0 and wa

  • The consequence of the derived degeneracy


Motivations

Motivations

  • General Property of scalar field dynamics

  • scalar field as dark energy: Tracking solutions

  • Tracker fields (Steinhardt etal, PRD 1999)


Tracking solutions

Tracking Solutions


Tracking solution general property

Tracking Solution: General Property

  • Almost independent of initial conditions

  • Relation

  • Common Dynamics for scalar fields


Efstathiou parametrization

Efstathiou Parametrization

  • Dark energy parametrization: capture the main dynamics of scalar field

MNRAS 383, 879 (1999)


Cpl parametrization

CPL Parametrization

  • Approximation

E. Linder

astro-ph/0210217


The degeneracy in cpl model

The degeneracy in CPL model

  • w0 and wa is degenerated

  • What is the degeneracy? related with ?


Dark energy parametrizations partial lists

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


Scalar field approximation

Scalar Field approximation

  • Cosmological equations


Scalar field dynamics

Scalar Field Dynamics

  • Take the (Slow-roll) approximation

  • For Thawing scalar field

Scherrer & Sen 2008, PRD 77, 083515


Approximation

approximation


Thawing scalar fields

Thawing scalar fields

  • Approximate w(z)

dotted curve

short dash curve

long dash curve


The degeneracy between and

The degeneracy between and

  • Relation

  • 0th order approximation

Scherrer and Sen 2008, PRD 78, 067303


Sslcpl model

SSLCPL model

  • Taylor Expansion

Gong etal., Int. J. Mod. Phys. 22 (2013) 1350035, 1301.1224


The accuracy of the approximation

The accuracy of the approximation


Sswcpl model

SSWCPL model

  • Take approximation


The accuracy of the approximation1

The accuracy of the approximation


The degeneracy

The degeneracy

  • Self-consistency


Flat sslcpl results

Flat SSLCPL Results


Flat sswcpl results

Flat SSWCPL Results


Flat cpl results

Flat CPL Results


Comparisons

Comparisons


Conclusions

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)


Thank you

THANK YOU!


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