l. perivolaropoulos leandros.physics.uoi.gr department of physics university of ioannina

51
L. Perivolaropoulos http://leandros.physics.uoi.gr Department of Physics University of Ioannina Open page

Upload: tuyen

Post on 06-Jan-2016

27 views

Category:

Documents


0 download

DESCRIPTION

Open page. Crossing the Phantom Divide: Observational Status and Theoretical Implications. L. Perivolaropoulos http://leandros.physics.uoi.gr Department of Physics University of Ioannina. Talk Made in Corfu-Greece Summer 2006. Main Points. - PowerPoint PPT Presentation

TRANSCRIPT

Page 1: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

L. Perivolaropouloshttp://leandros.physics.uoi.gr

Department of Physics

University of Ioannina

Open page

Page 2: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

Talk Made in Corfu-Greece

Summer 2006

Page 3: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

Dark Energy Probes include-SnIa (Gold sample and SNLS), -CMB shift parameter (WMAP 3-year), -Baryon Acoustic Oscillation Peak in LSS surveys, -Cluster gas mass fraction, -Linear growth rate from 2dF (z=0.15)

Some of these probes mildly favor an evolving w(z) crossing the phantom divide w=-1 over ΛCDM

Minimally Coupled Quintessence is inconsistent with such crossing

Scalar Tensor Quintessence is consistent with w=-1 crossing

Extended Gravity Theories (DGP, Scalar Tensor etc) predict unique signatures in the perturbations growth rate

Boisseau, Esposito-Farese, Polarski, Starobinsky 2000LP 2005

Page 4: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

2 8

3 m

GH a a a

DirectlyObservable

DirectlyObservable

Dark Energy(Inferred)

NoYes

2

2 8

3 m

a GH a a

a

Flat

Friedmann Equation 3~ taV

mm

Not Consistent

Page 5: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

emptyL

L

d

dlog5

emptyL

L

d

dlog5

z~0.5: Acceleration starts

1

( )1

1Ld za d

z H za c dz z

157 SnIa

from Spergel et. al. 2006

Q: What causes this accelerating expansion?Flat

Page 6: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

3 3

3 1~X w

X

d a p d aa

p w

322 0

02

320 0

8( )

3

1

m

m X

aa GH z a

a a

H z z

00 0.2 0.3mm

crit

(from large scale structure observations)

crit

1

'3 (1 ( '))

'~

ada

w aa

e

Friedman eqn I: 41 3

3X

m

p a Gw w

a

Friedman eqn II:

1 Negative Pressure

3w

Page 7: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

10 10( )2.5log ( ) 25 5log

( )L obs

L d zm z M Mpcl z

2

3 22 20 02

( ) 1 1m k

aH z H z z

a

0 1 m k

0

0 00

1( ) sin 1

; ,1

z

L th mmm

c z H dzd z

H zH

2

1022

1

5log ( ) 5log ( ; , ), min

L i obs L i m th

mi

N

i

d z d z

Page 8: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

SNLS

TruncatedGold

GoldSample

S. Nesseris, L.P. Phys. Rev. D72:123519, 2005

astro-ph/0511040

Page 9: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

0

02 2

min

2 2min

1 2

: 1 2

1 2

: 1 21 2

1 2

2min

; , ,...,

; , ,...,

; , ,...,

; , ,...,, ,...,

; , ,...,

z

z

obsL i

obsL i

dz

n

dzData d zth

L n

n

Data d z L nn

n

Physical Model H z a a a ansatz

d z a a a

H z a a a

d z a a aa a a

w z a a a

1 2, ,..., na a a

Page 10: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

z

zwwzw

1)( 10 Chevalier-Polarski 2001, Linder 2003

20 1 2( ) 1 1z a a z a z Sahni et. al. 2003

1( )2i

i ii

ww z z z z z Huterer-Cooray 2004

0 1 2 3( ) cosz a a a z a Nesseris-LP 2004

3 1

0( ) 1w

z a z Constant w

0 1( ) w z w w z Weller-Albrecht 2002

2

300

2 ln1 1( ) 3

( )1 1

X

Xm

d Hzp z dzw z

z Hz

H

( ) tanh2 2

T

z

w w w w z zw z

Pogosian et. al. 2005

Page 11: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

2min 171.7OA

LCP

2min 177.1CDM

0.3m

• All best fit parameterizations cross the phantom divide at z~0.25

• The parametrization with the best χ2 is oscillating

Lazkoz, Nesseris, LP 2005

Page 12: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina
Page 13: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

Espana-Bonet, Ruiz-Lapuenteastro-ph/0503210

Wang, Lovelace 2001Huterer, Starkman 2003Saini 2003Wang, Tegmark 2005Espana-Bonet, Ruiz-Lapuente 2005

Q: Do other SnIa data confirm this trend?

Page 14: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

Trunc. Gold (140 points, z<1) Full Gold (157 points, z<1.7)SNLS (115 points z<1)

SNLS data show no trend for crossing the phantom divide w=-1!

0.24m z

zwwzw

1)( 10

S. Nesseris, L.P. Phys. Rev. D72:123519, 2005

astro-ph/0511040

Page 15: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

Definition:

1 1

1 1

A recTT TT

s rec s rec A recTT TT

A rec s rec A rec

s rec

d zr z r z d zl

Rd zl r z d z

r z

11

2 2 2 2

1~ : Peak Location of Corresponding SCDM model:

1, ,

TT

m b b m m

l

h h h h

11

1~ : Peak Location of considered model or data TTl

5 10 50 100 500 1000mult. number l

1000

1500

2000

3000

5000

ll1C lTT2K̂2

2201 TTl 1' 246TTl

14.0 ,022.0 ,043.0 ,27.0 22 hh mbbm

2 21, 0.157, 0.022, 0.14m b b mh h

1 1

12 2

1

0

21

''

rec

TTs rec A rec

r r recz TTs rec A rec

m

r z d z lR a

r z d z ldzE z

recs ar

A recd a1

1

2 2

2 1/ 2 200 0

rec reca as s r

sm m

c a da c a da hr a

a H a H h

1

200

rec

rec

z

A rec rec rec

a

c da dzd z a c a

a H a H E z

1 1

2 2

0

2 1rec

A rec r r rec

c ad z a

H

1

2 2

2 200 0

rec reca as s r

sm

c a da c a da hr a

a H a H h

Page 16: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

5 10 50 100 500 1000

mult. number l

1000

1500

2000

3000

5000

ll1C lTT2K̂2

1 220 0.8TTl 1' 246TTl

1 1

1 2 2

1

0

' 246 21.123 1

220 ''

rec

TT

r r reczTT

m

lR a

l dzE z

14.0 ,022.0 ,043.0 ,27.0 22 hh mbbm

2 21, 0.157, 0.022, 0.14m b b mh h

965.0

0

'' 1.7

'

recz

m

dzR

E z

Q: Does R contain all the info about H(z) in the CMB Spectrum?

Page 17: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

5 10 50 100 500 1000

mult. number l

1000

1500

2000

3000

5000

ll1C lTT2K̂2

0 10.27, 0.8, 0.0m w w

0 10.27, 0.9, 0.3m w w

0 10.27, 0.8, 0.0m w w

0 10.15, 1.32, 0.0m w w

0 10.50, 0.3, 0.02m w w

z

zwwzw

1)( 10

2 21.7, 0.022, 0.142 b mR h h

CMB Spectrum practically unaffected

All the useful H(z) related info coming fromthe CMB spectrum is contained in R.

10 1

13 13 3 12 2 1

0 0 0( ) 1 1 1ww w z

m mH z H z z e

Page 18: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.2m

Gold datasetRiess -et. al. (2004)

SNLS datasetAstier -et. al. (2005)

Other data:CMB, BAO, LSS, Clusters

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

S. Nesseris, L.P. in prep.

)(zw Other data:CMB, BAO, LSS, Clusters

z z z

2

300

2 ln1 1( ) 3

( )1 1

DE

DEm

d Hzp z dzw z

z Hz

H

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

Gold datasetRiess -et. al. (2004)

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

SNLS datasetAstier -et. al. (2005)

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

Other data:CMB, BAO, LSS, Clusters )(zw

z z z

0 0.3m

z

zwwzw

1)( 10

Minimize:

2 2 2 21 2 1 2 1 2 1 2

22 2 226

1 21 2 1 2 1 2

2 2 2 21

, , , , , ,

; ,, , 1.70 , , 0.469 0.15; , 0.51

0.03 0.017 0.11

CMB m BAO m cl LSS

SCDMgas i gas im m

i gas i

w w w w w w w w

f z w w fR w w A w w g z w w

0 0.2m

11.051.0)(

)('15.01

1

aD

aaD

azg

Eisenstein et. al. 2005Wang, Mukherjee 2006

Allen et. al. 20042dF:Verde et. al.

MNRAS 2002

Page 19: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

0 0.2m

0 0.3m

0.2mCMB BAO Clusters LSS

0.3mCMB BAO Clusters LSS

Page 20: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

What theory produces crossing of the w=-1?

Page 21: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

VL 2

2

1 +: Quintessence

-: Phantom

2

0

2

12 112

Vpw

V

To cross the w=-1 line the kinetic energy term must change sign

(impossible for single phantom or quintessence field)

Phant < 1

Quint 1

Generalization for k-essence:

Page 22: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

Non-minimal Coupling

1

, U ΦF

1F

1

8 effG

Page 23: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

p,

21

2 m mH p F HFF

2 21 13

3 2mH U HFF

Page 24: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

Minimum: Generic feature

F(Φ)

ΦΦ

U(Φ)

L.P. astro-ph/0504582, JCAP 0510:001,2005, S. Nesseris, L.P. astro-ph/0602053, Phys.Rev.D73:103511,2006

JCAP 0511:010,2005

Page 25: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

0

, 1

ma

a a D aa

Growth Factor:

Growth Factor Evolution (Linear-Fourier Space):

0,,

2

3,'

'3,'' 25

0

akDakf

aHaakD

aH

aH

aakD m

General Relativity: ( , ) 1 ( , ) ( )f k a D k a D a

DGP: 0

1 ( ) '( )( , ) 1 , 1 1

3 3 ( )rc

H a H a af k a

a H H a

Scalar Tensor: 0( , ) ( ) 1 1f k a G a G a

Modified Poisson: 2

1( , ) 1

1 s

f k akra

0 )( aaaD

Koyama and Maartens (2006)

Sealfon et. al. (2004)

Boisseau, Esposito-Farese, Polarski Staroninski (2000)

Uzan (2006)

Page 26: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

0 0.2 0.4 0.6 0.8 1a

0.4

0.5

0.6

0.7

0.8

0.9

1

ga

ΛCDM (SnIa best fit, Ωm=0.26)

DGP SnIa best fit

+Flat Constraint

Scalar Tensor (α=-0.5, Ωm=0.26)

Flat Matter Only

11.051.0)(

)('15.01

1

aD

aaD

azg

Verde et. al. MNRAS 2002Hawkins et. al. MNRAS 2003

'( )

( )

aD ag a

D a

Page 27: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

• Interesting probes of the dark energy evolution include: - SnIa (Gold sample, SNLS)- CMB shift parameter- Baryon Acoustic Oscillations (BAO) Peak of LSS correlation (z=0.35)- Clusters X-ray gas mass fraction- Growth rate of perturbations at z=0.15 (from 2dFGRS)

• All recent data indicate that w(z) is close to -1. Thus w(z) may be crossing the w=-1 line.

• Minimally Coupled Scalar predicts no crossing of w=-1 line

• Scalar Tensor Theories are consistent with crossing of w=-1

• Extended Gravity Theories (DGP, Scalar Tensor etc) predict uniquesignatures in the growth rate of cosmological perturbations

Page 28: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

rF

F

G

rG 0

0

Page 29: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

SnIa peak luminosity:

SnIa Absolute Magnitude Evolution:

SnIa Apparent Magnitude:

with:

Parametrizations:

Page 30: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

0 0.2 0.4 0.6 0.8 1a

0.2

0.4

0.6

0.8

1

Da

0 10.27, 0.8, 0.0m w w

0 10.27, 0.9, 0.3m w w

0 10.27, 0.8, 0.0m w w

0 10.15, 1.32, 0.0m w w

0 10.50, 0.3, 0.02m w w

z

zwwzw

1)( 10

0

, 1

ma

a a D aa

Growth Factor:

0

25

'3 3'' ' 0

2m

H aD a D a D a

a H a a H a

0 )( aaaD

Models degenerate in ISW are also degenerate in linear growth factor.

Page 31: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

Hubble free luminosity Distance

Apparent Magnitude:

χ2 depends on M:

: MinExpand where

Minimize:

Page 32: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

Gold Sample SNLS

Uniform Analysis of Data (light curves) by one Group

Uniform Analysis of Data (light curves) by one Group

Combination of Data from Various Instruments

Use of a single ground based instrument (megaprime of

CFH 3.6m telescope)

Redshift Range 0<z<1.7 Redshift Range 0<z<1

157 datapoints 73 new datapoints

Page 33: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

, ,

1

230

0

, , ,

1 ( , ),

1

ln ,21 1

3,

1 1

iK z z sL i L L i i

d ss Ldz

s

dsdz

m

Data d z d z d z K z z

d d zH z

c dz z

d H zz

dzw zH

zH

smoothing scale

Wang, Lovelace 2001Huterer, Starkman 2003Saini 2003Wang, Tegmark 2005Espana-Bonet, Ruiz-Lapuente 2005

Page 34: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

Fisher Matrix: 1121

12121

2122

,,,,,

2

1wwCwwAwwAwwA

ww

wwijijijij

ji

Covariance Matrix

1 2,i i iiw w C w w Parameter Estimation:

w(z) plot with error regions: 0 1( )1

zw z w w

z

, , , ,

2

1 1 2, 1

( ) ,i j i j i j i j

iji j i jw w w w

w z w zw z w z C w w

w w

Page 35: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

from Max Tegmark's home page

Page 36: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

zH

zcABx

0

z dz

x CD x cH z

Effective Scale:

1/321/32

0

zz z

V

c z dzD z x x c

H z H z

soundpeakLCDM

V

Vpeak

zH rrzD

zDrrz LCDM

35.0

35.0,

MpczDV 64137035.0

200.35

0.469 0.0170.35

V mD z HA

c

Correlation function:

Page 37: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

Minimize: 2 2

1 2 1 22 21 2 1 2 2 2

, , 1.70 , , 4.69, , , ,

0.03 0.17m m

CMB m BAO m

R w w A w ww w w w

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

Assume:z

zwwzw

1)( 10

zw

z

0.25m

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

z

0.3m

zw

Page 38: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

m

b

tot

gasbgas M

Mf

gastot

gasb

tot

b

m

b fM

M

M

Mb 11

Global Mass Fraction vs Baryon Gas Mass fraction:

Isothermal Gas Model: 513/ 2 2 2... , , , , , ,c

b gas e c X e c X ArM R B T r L R C T l z d zR

zdAc 2

4 L Xd z l R

cO

Cluster

Hydrostatic Equilibrium: ... tot e AM R D T d z

Define Cluster Baryon Gas Mass fraction:

Page 39: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

Cluster Baryon Gas Mass fraction:

3 32 2, , ... gas

gas A c e Atot

M R Cf d z Q T d z

M R D

Connect to Global Mass fraction:

3

21 1 bgas i A i

m

b f Q d z

Define:

SCDMgas iSCDM SCDM

gas i i A i i SCDMA i

f zf z Q d z Q

d z

Observed

23

1

iA

iSCDMA

m

bi

SCDMgas zd

zdbzf

Data

SCDM LCDM

32

1

1b

gas i A im

f Q d z

Page 40: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

Minimize: 226

1 221 2 2

1

; ,,

SCDMgas i gas i

cli gas i

f z w w fw w

Assume: z

zwwzw

1)( 10

0 0.25 0.5 0.75 1 1.25 1.5 1.75

6

5

4

3

2

1

0

1

0 0.25 0.5 0.75 1 1.25 1.5 1.75

6

5

4

3

2

1

0

1

0 0.25 0.5 0.75 1 1.25 1.5 1.75

6

5

4

3

2

1

0

1

0 0.25 0.5 0.75 1 1.25 1.5 1.75

6

5

4

3

2

1

0

1

zw zw

z z

0.25m 0.3m

Page 41: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

25.0 mBAOCMB

zw

z0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0.25mCMB BAO Clusters

zw

z

2 2CMB BAO

2 2 2CMB BAO cl

Page 42: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

0

, 1

ma

a a D aa

Growth Factor:

Growth Factor Evolution (Linear-Fourier Space):

0,,

2

3,'

'3,'' 25

0

akDakf

aHaakD

aH

aH

aakD m

General Relativity: ( , ) 1 ( , ) ( )f k a D k a D a

0 )( aaaD

Page 43: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

0.2 0.4 0.6 0.8 1a

0.25

0.5

0.75

1

1.25

1.5

1.75

2

ga 11.051.0)(

)('15.01

1

aD

aaD

azg

Verde et. al. MNRAS 2002Hawkins et. al. MNRAS 2003

'( )

( )

aD ag a

D a

1 20.25, 0.8, 0.0m w w

1 20.25, 0.9, 0.3m w w

1 20.25, 1.0, 0.59m w w

1 20.25, 3, 0.0m w w

1 20.25, 0.5, 0.0m w w

z

zwwzw

1)( 10

Page 44: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

Minimize: 21 221 2 2

0.15; , 0.51,

0.11LSS

g z w ww w

Assume: z

zwwzw

1)( 10

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

25.0 mBAOCMB

zw

z0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0.25mCMB BAO LSS 2 2CMB BAO 2 2 2

CMB BAO LSS

Page 45: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

dz

d'

positive energy of gravitons

Page 46: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina
Page 47: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina
Page 48: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

For U(z)=0 there is no acceptable F(z)>0 in 0<z<2 consistent with

the H(z) obtained even from a flat LCDM model.

0 0.2 0.4 0.6 0.8 1z

0.75

0.5

0.25

0

0.25

0.5

0.75

1

F

Page 49: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

SNLS

TruncatedGold

FullGold

S. Nesseris, L.P. Phys. Rev. D72:123519, 2005

astro-ph/0511040

2

1022

1

5log ( ) 5log ( ; , ),

L i obs L i m th

mi

N

i

d z d z

Minimize:

Page 50: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

Fisher Matrix: 1121

12121

2122

,,,,,

2

1wwCwwAwwAwwA

ww

wwijijijij

ji

Covariance Matrix

1 2,i i iiw w C w w Parameter Estimation:

w(z) plot with error regions: 0 1( )1

zw z w w

z

, , , ,

2

1 1 2, 1

( ) ,i j i j i j i j

iji j i jw w w w

w z w zw z w z C w w

w w

Page 51: L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina

0.078 0.189 0.011

0.088 0.184 0.011

0.143 0.167 0.019

0.188 0.169 0.011

0.206 0.180 0.015

0.2 0.4 0.6 0.8

0.080.1

0.120.14

0.160.18

0.2