Post on 31-Mar-2015
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