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

Motivations: General Property of Scalar Field dynamics

Dark energy parametrizations

The degeneracy between w0 and wa

The consequence of the derived degeneracy

Motivations

General Property of scalar field dynamics scalar field as dark energy: Tracking

solutions

Tracker fields (Steinhardt etal, PRD 1999)

Tracking Solutions

Tracking Solution: General Property

Almost independent of initial conditions Relation

Common Dynamics for scalar fields

Efstathiou Parametrization Dark energy parametrization: capture the main dynamics of scalar field

MNRAS 383, 879 (1999)

CPL Parametrization

Approximation

E. Linderastro-ph/0210217

The degeneracy in CPL model

w0 and wa is degenerated

What is the degeneracy? related with ?

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

Cosmological equations

Scalar Field Dynamics

Take the (Slow-roll) approximation

For Thawing scalar field

Scherrer & Sen 2008, PRD 77, 083515

approximation

Thawing scalar fields

Approximate w(z)

dotted curve

short dash curve

long dash curve

The degeneracy between and

Relation

0th order approximation

Scherrer and Sen 2008, PRD 78, 067303

SSLCPL model

Taylor Expansion

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

The accuracy of the approximation

SSWCPL model

Take approximation

The accuracy of the approximation

The degeneracy

Self-consistency

Flat SSLCPL Results

Flat SSWCPL Results

Flat CPL Results

Comparisons

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！