Probing the curvature and dark energy

Gong, Yungui

龚云贵

Chongqing University of Posts and Telecommunications

重庆邮电学院

2005 International Summer School/Institute on Particle Physics, Astrophysics and Cosmology (Section II) ， August 16, 2005

• Dark Energy Introduction

• Introduction to SN Fitting Method

• Current Status of Parameterizations

• One-parameter Parameterization

• Comments

• Conclusion

Why Dark Energy? 03.175

98.0

46.0

2

26.031.0

15.017.00

m

Riess etal. astro-ph/0402512

Introduction to SN Fitting Method

z

L

L

uH

duztacdtzarzad

dMm

000

100

)()1()(/)1()1(

Mpc)/(log525

Assume flat universe and Robertson-Walker metric

Mpc]/)(

)1[(log5250100 z

uH

duzMm

i i

ii zz2

2calobs2 )]()([

)3(3

4

)(2

1

)(2

1

)1(

)(3

8

2

2

30

2

QQm

Q

Q

mm

Qm

pG

a

a

Vp

V

z

GH

The SNe Ia data in Riess etal. lists the distance moduli μ0,Using the least square fit, we can reconstruct the functionH(z) in general.

In standard model, we know

])1([

3

8

30

20

2

20

,,

zHH

H

G

m

QmQm

MarginalizationSince appears linearly in the form of

in , so the marginalization by integrating over all possible values of is equivalent to finding the value of which minimizes if we also include the suitable integration constant and measure function,

0H 010log5 H

2

2/2eL

2

0H

0H

Parameterizations

• Taylor expansion of Hubble parameter, M. Visser, CQG 21 (2004) 2603

• Prameterizations of energy density: 2nd Order Polynomial, U. Alam etal. MNRAS 354 (2004) 275

• Negative Power Polynomial, U. Alam etal. MNRAS 354 (2004) 275

1))1()1((3

)1(2)1(,)1()1(

2210

2212

210

zAzAA

zAzAzAzAA QQ

1))1()1()1((3

)1()1(,)1()1/(

31

201

13

1110

zBzBzB

zBzBzBzBB QQ

Common Parameterization of WQ

• Constant equation of state w

• Linear equation of state w=w0+w1z

• Stable Parameterizations

• Wetterich Parameterization

• Parameterization

20)))1ln(1/(1(3

0 ))1ln(1(,)1( 0

zbz Q

zbQQ

z

zez a

Qzz

QQaa

1,)1( 0)1/(3)1(3

00

)1ln(1,))1ln(1()1( 0/33

00

zbzbz Q

bQQ

20)1(2/3)1(3

0 )1(,)1(

220

z

zez a

Qzz

QQa

H.K. Jassal, MNRAS 356(2005) L11

Fitting Results

• Taylor expansion of Hubble parameter

Y. Gong, astro-ph/0405446 , Class. Quantum Grav. 22 (2005) 2121

1))1()1((3

)1(2)1(,)1()1(

2210

2212

210

zAzAA

zAzAzAzAA QQ

1))1()1()1((3

)1()1(,)1()1/(

31

201

13

1110

zBzBzB

zBzBzBzBB QQ

z

zez a

Qzz

QQaa

1,)1( 0)1/(3)1(3

00

20)1(2/3)1(3

0 )1(,)1(

220

z

zez a

Qzz

QQa

20)))1ln(1/(1(3

0 ))1ln(1(,)1( 0

zbz Q

zbQQ

)1ln(1,))1ln(1()1( 0/33

00

zbzbz Q

bQQ

Supernova Fit to dark energy

One parameter Parameterization

z

wzw

1

)( 0

zzez

wzw

1/0

1)(

Y. Gong and Y.Z. Zhang, astro-ph/0502262, PRD in press

4.175

2.01.1

05.001.0

05.025.0

2

0

0

0

wk

m

z

wzw

1

)( 0

5.176

97.0

001.0

04.028.0

2

17.019.00

046.0045.00

0

w

k

m

zzez

wzw

1/0

1)(

Results

Summary

Comments

• What can we say about acceleration?• (Starkman, Trodden and Vachaspati)

Dark Energy with constant EOS

Y. Gong and Y.Z. Zhang, gr-qc/0508053

Conclusion

Thanks!