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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 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

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

sswcpl model
SSWCPL model
  • Take approximation
the degeneracy
The degeneracy
  • Self-consistency
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)