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!