direct evidence of acceleration from a distance modulus- redshift graph
DESCRIPTION
Direct Evidence of acceleration from a distance modulus- redshift graph. Yungui Gong 龚云贵 College of Mathematics and Physics Chongqing University of Posts and Telecommunications 重庆邮电大学数理学院. String Theory and Cosmology Workshop , KITPC, 10/22/2007. Outlines. Introduction SN Ia Evidence - PowerPoint PPT PresentationTRANSCRIPT
Direct Evidence of acceleration from Direct Evidence of acceleration from a distance modulus-redshift grapha distance modulus-redshift graph
Yungui Gong 龚云贵
College of Mathematics and Physics
Chongqing University of Posts and Telecommunications
重庆邮电大学数理学院
String Theory and Cosmology Workshop , KITPC, 10/22/2007
OutlinesOutlinesIntroductionSN Ia EvidenceIntroduction to numerical Fitting Dark Energy ParameterizationConclusion
Dark EnergyDark Energy
Quintessence?Quintessence?
Dark EnergyDark Energy
Type Ia Supernova Type Ia Supernova ObservationObservationObservational Data: Redshift-Luminosity distance
For a given cosmological model, calculate Luminosity distance-redshift relation
To fit observation data, need to assume a model and then fit the parameters in the model
Dark EnergyDark Energy
SN Ia EvidenceSN Ia Evidence
Model: Cosmological constantModel independent Way? Energy Condition
Friedmann EquationFriedmann Equation
Friedmann Equation
0)(3
)3(3
43
82
2
pH
pG
a
a
G
a
kH
Acceleration and Energy Acceleration and Energy ConditionsConditions
Energy Conditions in Distance Energy Conditions in Distance graphgraphStrong Energy Condition
03 p
0 p
Results?Results?The SEC was first violated billions of
years ago, at z~1.1 (Santos etal., PRD 74 (06) 067301; PRD 75(07) 083523 ) .
03 p
CDM ModelCDM ModelDeceleration to Acceleration
Transition happened at z<0.8
How to interpret? How to interpret? Gong and Wang, JCAP 0708 (07)
018; PLB 652 (07) 63Key Points: SEC and the derived
luminosity conditions are not equivalent!
ReasonsReasonsIntegration Effect
Key PointsKey Points
SEC leads to upper bound on the luminosity distance
Violation of the upper bound means violation of SEC
Violation of the upper bound at z does not necessarily mean the violation of SEC at the same z
Satisfaction of the upper bound up to z does not mean no violation of SEC up to z
)1ln()1()(03 0 zzzdHp L
ConclusionConclusionEnergy condition can
be used to give direct and model-independent evidence of cosmic acceleration
No detailed information about the acceleration can be given
No information on dark energy can be given
Parameter DegeneracyParameter Degeneracy
At Low Red-shift (z<0.1), Almost the same (z)–z relation
To the first order, w(z=0)
zHzdL )( 0
Numerical FittingNumerical FittingFor a given cosmological model, we can calculate
the luminosity distance (or distance modulus) with given parameters P
Find out the parameters that gives the minimum value of
Parameter space: grid (point to point search), Monte Carlo Markov Chain method
)|( PzdL)|( Pz
2
22 -)|(
obsPz
Toy Model (Essence Data)Toy Model (Essence Data)
85.043.1 :3
59.0,12.1 ,17.195
0
02
w
ww a
c
a
c z
w
z
www
110
2
1.0 ,59.0 ,12.10 ca zww
88.196,4.0)0(
12.196,0.2)0(2
1
21
zww
zww
The error of The error of ww((zz=0)=0)
The sweet spotThe sweet spot
结论结论
Energy condition can be used to give direct and model-independent evidence of cosmic acceleration
The luminosity distance is almost independent of cosmological models at low redshift, so the value of w(z=0) may not be well determined.
Thank youThank you!!