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

Department of Physics

University of Ioannina

Open page

Talk Made in Corfu-Greece

Summer 2006

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

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

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

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

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

SNLS

TruncatedGold

GoldSample

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

astro-ph/0511040

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

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

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

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?

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

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

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?

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

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

0 0.2m

0 0.3m

0.2mCMB BAO Clusters LSS

0.3mCMB BAO Clusters LSS

What theory produces crossing of the w=-1?

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:

Non-minimal Coupling

1

, U ΦF

1F

1

8 effG

p,

21

2 m mH p F HFF

2 21 13

3 2mH U HFF

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

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)

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

• 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

rF

F

G

rG 0

0

SnIa peak luminosity:

SnIa Absolute Magnitude Evolution:

SnIa Apparent Magnitude:

with:

Parametrizations:

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.

Hubble free luminosity Distance

Apparent Magnitude:

χ2 depends on M:

: MinExpand where

Minimize:

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

, ,

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

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

from Max Tegmark's home page

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:

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

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:

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

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

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

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

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

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

dz

d'

positive energy of gravitons

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

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:

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

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