on the degeneracy between w 0 and w a
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/1.jpg)
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
![Page 2: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/2.jpg)
Contents
Motivations: General Property of Scalar Field dynamics
Dark energy parametrizations
The degeneracy between w0 and wa
The consequence of the derived degeneracy
![Page 3: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/3.jpg)
Motivations
General Property of scalar field dynamics scalar field as dark energy: Tracking
solutions
Tracker fields (Steinhardt etal, PRD 1999)
![Page 4: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/4.jpg)
Tracking Solutions
![Page 5: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/5.jpg)
Tracking Solution: General Property
Almost independent of initial conditions Relation
Common Dynamics for scalar fields
![Page 6: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/6.jpg)
Efstathiou Parametrization Dark energy parametrization: capture the main dynamics of scalar field
MNRAS 383, 879 (1999)
![Page 7: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/7.jpg)
CPL Parametrization
Approximation
E. Linderastro-ph/0210217
![Page 8: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/8.jpg)
The degeneracy in CPL model
w0 and wa is degenerated
What is the degeneracy? related with ?
![Page 9: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/9.jpg)
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
![Page 10: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/10.jpg)
Scalar Field approximation
Cosmological equations
![Page 11: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/11.jpg)
Scalar Field Dynamics
Take the (Slow-roll) approximation
For Thawing scalar field
Scherrer & Sen 2008, PRD 77, 083515
![Page 12: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/12.jpg)
approximation
![Page 13: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/13.jpg)
Thawing scalar fields
Approximate w(z)
dotted curve
short dash curve
long dash curve
![Page 14: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/14.jpg)
The degeneracy between and
Relation
0th order approximation
Scherrer and Sen 2008, PRD 78, 067303
![Page 15: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/15.jpg)
SSLCPL model
Taylor Expansion
Gong etal., Int. J. Mod. Phys. 22 (2013) 1350035, 1301.1224
![Page 16: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/16.jpg)
The accuracy of the approximation
![Page 17: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/17.jpg)
SSWCPL model
Take approximation
![Page 18: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/18.jpg)
The accuracy of the approximation
![Page 19: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/19.jpg)
The degeneracy
Self-consistency
![Page 20: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/20.jpg)
Flat SSLCPL Results
![Page 21: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/21.jpg)
Flat SSWCPL Results
![Page 22: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/22.jpg)
Flat CPL Results
![Page 23: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/23.jpg)
Comparisons
![Page 24: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/24.jpg)
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)
![Page 25: On the degeneracy between w 0 and w a](https://reader035.vdocuments.mx/reader035/viewer/2022062410/56815989550346895dc6cb97/html5/thumbnails/25.jpg)
THANK YOU!