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Firenze 2011
Luca Amendola
ITP, University of Heidelberg
Accuracy cosmology or, Testing DE with future surveys
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Euclid Surveys – Simultaneous (i) visible imaging (ii) NIR photometry (iii) NIR spectroscopy
– 15,000 square degrees
– 100 million redshifts, 2 billion images
– Median redshift z = 1
– PSF FWHM ~0.18’’
– >800 peoples, >10 countries
Euclid in a nutshell
Euclid satellite
Firenze 2011
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Firenze 2011
Euclid twin probes
15,000 square degrees 70,000,000 galaxy redshifts 0.5 < z < 2
15,000 square degrees 40 galaxy images per sq. arcmin 0.5 < z < 3
P(k,z) Weak lensing
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Firenze 2011
Precision is nothing without accuracy
1
The power of statistics (collaboration E. Branchini, C. di Porto, C. Quercellini,
V. Pettorino, A. Vollmer)
2
Lensing and supernovae (collab. V. Marra, M. Quartin, J. Kannulainen)
3
Homogeneity and isotropy (collab. C. Quercellini, M. Quartin)
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Firenze 2011
Two free functions
)])(21()21[( 222222 dzdydxdtads
At linear order we can write:
Poisson’s equation
anisotropic stress
2 24 m mGa 2 2 ( ,4 ) m mQ aa kG
0
( , )k a
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Firenze 2011
Modified Gravity at the linear level
scalar-tensor models 2
2
2
2
0,
*
'
')(
'32
)'(2)(
FF
Fa
FF
FF
FG
GaQ
cav
0),(
1),(
ak
akQ
standard gravity
DGP
13
2)(
21;3
11)(
a
wHraQ DEc
f(R) Ra
km
Ra
km
a
Ra
km
Ra
km
FG
GaQ
cav
2
2
2
2
2
2
2
2
0,
*
21
)(,
31
41
)(
Lue et al. 2004; Koyama et al. 2006
Bean et al. 2006 Hu et al. 2006 Tsujikawa 2007
coupled Gauss-Bonnet
see L. A., C. Charmousis, S. Davis 2006 ...)(
...)(
a
aQ
Boisseau et al. 2000 Acquaviva et al. 2004 Schimd et al. 2004 L.A., Kunz &Sapone 2007
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Firenze 2011
Reconstruction of the metric
v Hv
dzperp )(
massive particles respond to Ψ
massless particles respond to Φ-Ψ
2 2 2 2 2 2[(1 2 ) (1 2 )( )]ds a dt dx dy dz
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Firenze 2011
Peculiar velocities
'v
' f
b b
Correlation of galaxy velocities:
galaxy peculiar field
redshift distortion parameter
2 2( , ) (1 ) ( ), cosz rP k P k
Kaiser 1987
cosm . .pec velz z z
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Firenze 2011
Clustering in redshift and momentum
space
2 2 2( , , ) ( )(1 ) ( )z rP k z G z P k
baryon oscillations
redshift distortions
Current data
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Firenze 2011
Euclid + Bayes + Fisher
1
1
2
2
2 1),(
),(),(ln),(ln
8
1 max
minsurvey
k
kji
ij VknP
knPkPkPdkkdF
)()(2
1exp
)(
2
1exp
)()(
2
2
jF
jijiF
i
i
jti
i
FNL
PPNP
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Firenze 2011
Euclid beyond w
• Growth rate (mod. gravity) • Sound speed • Dark energy coupling • Early dark energy • Ultra-light fields • Neutrino mass and generations • Non-gaussianity • ….
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Firenze 2011
On growth, bias and amplitude
It is sometimes stated that galaxy clustering alone cannot constrain at the same time the growth rate, the σ8 and the bias since they are degenerate. However, if they are parametrized this is no longer true.
Plot sigma8 gamma
C. Di Porto, E. Branchini, L.A. 2011
f
2 2 2 2 2
8
2 ( ) ln2 2 2 2
8
2 ( ) ln2 2 2 2 2
8
( )( , , ) ( ) ( ) (1 ) ( )
( )
( )( ) (1 ) ( )
( )
( ) ( ) (1 ( ) ) ( )m
z r
f z d a
r
z d a
m r
f zP k z G z b z P k
b z
f zb z e P k
b z
z e z z P k
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Firenze 2011
Growth rate & modified gravity
0),(2
3)'
1('' akQH
Hm
Tsujikawa et al. 2009
m
ad
ds
log
log
Peebles fit is not accurate in general !
222
2221
kMa
kQ
Standard Peebles fit
For scalar-tensor and f(R) and DGP etc.
f(R)
''3
'2
f
fM
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Firenze 2011
reconstructing f(R)
m
ad
ds
log
log
)2411(4
1~
6~
41
3~
21
~
log
log
wQ
wQ
Qad
ds m
A
growth rate s one-parameter
general fit
7.0A
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Firenze 2011
E.g. f(R)
...
tanh
1
)1/(
)()(
1
1
1
22
1
1
f
xf
ef
xxf
xfRRRf
x
nn
c
accuracy
Di Porto, Quartin & LA 2011
models
m
AQzks ~
),( 1 or 2 fit parameters
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Firenze 2011
Present constraints on gamma
C. Di Porto & L.A. Phys.Rev. 2007
DGP
LCDM
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Firenze 2011
Euclid’s challenge
Growth of matter fluctuations
C. Di Porto & L.A. 2010
Euclid error forecast
Present error
Growth rate
C. Di Porto, L.A., E. Branchini 2011 2 2 2 2
, ,
'( , , ) ( ) ( )(1 ) ( , 0)g z m rP k z G z b z P k z
b
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Firenze 2011
Euclid forecasts, I
Euclid current vs. Euclid
C. Di Porto, L.A., E. Branchini 2011
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Firenze 2011
Euclid forecasts, II
E.g. LCDm and wCDM predicts* negative γ1, while DGP predicts positive γ1
*Gannouji, et al. 2009
f(R)
DGP
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Firenze 2011
Euclid forecasts, III
D. Sapone, L.A., M. Kunz 2010
Effects of DE sound speed on matter clustering
mm
DEDE
mmDEDEmm
akQ
akQGaGak
1),(
),(4)(4 222
Cold dark energy!
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Firenze 2011
Euclid forecasts, IV
Coupled dark energy
Effects on CMB, growth rate, BAO peaks, etc
growth
CMB
BAO
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Firenze 2011
Euclid forecasts, IV
Coupled dark energy
Put combined constraints
CMB+P(k)+WL
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Firenze 2011
Euclid forecasts, IV
Coupled dark energy
Combined constraint on coupling
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Firenze 2011
Precision is nothing without accuracy
1
The power of statistics (collaboration C. di Porto, A. Vollmer)
2
Lensing and supernovae (collab. V. Marra, M. Quartin, J. Kannulainen)
3
Homogeneity and isotropy (collab. C. Quercellini, M. Quartin)
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Firenze 2011
Observer
Dark matter halos
Background
sources
Lensing of distant sources
SNIa are standard candles but: - Intrinsic magnitude scatter - Lensing magnitude scatter
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Firenze 2011
Lensing of distant sources
Marra & Kainulainen 2009
Lens parameters: Halo mass and concentration
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Firenze 2011
Biasing the estimates
Distribution of SN deviations from
the mean in presence of lensing
The lensing distribution depends on Redshift and on cosmological model!
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Firenze 2011
Biasing the SN estimates
L. A., J. Kannulainen, V. Marra,
M. Quartin, Phys Rev Lett 2010
No lensing
Lensing
Non-linear/non-gaussian effects
can significantly bias the estimates
of cosmological parameters
Union data set Kowalsky et al. 2008
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Firenze 2011
Precision is nothing without accuracy
1
The power of statistics (collaboration C. di Porto, A. Vollmer)
2
Lensing and supernovae (collab. V. Marra, M. Quartin, J. Kannulainen)
3
Homogeneity and isotropy (collab. C. Quercellini, M. Quartin)
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Firenze 2011
Cosmic Degeneracy
void model
Garcia-Bellido & Haugbolle 2008
Tomita 2001 Celerier 2001 Alnes & Amarzguioi 2006,07 Bassett et al. 07 Clifton et al. 08 Notari et al. 2005-08 Marra et al. 08 Garcia-Bellido & Haugbolle 2008
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Firenze 2011
One null cone
0H
1z
0znow
time
comoving dist. 0H
z
zHa
1
)(
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Firenze 2011
One null cone
inH
1z
0znow
VOID
time
com. dist. outH
One null cone
z
rzHa
1
),(
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Firenze 2011
Two null cones are better than one!
)(zH1z
0znow
VOID
time
com. dist. ttnow
inHoutH
Mashhoon & Partovi 1985 Uzan, Clarkson & Ellis 2007 Quartin, Quercellini, L.A. 2009
z
rzHa
1
),(
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Firenze 2011
Sandage 1962
yearcmv sec//1
)( 1zH )( 2zH
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Firenze 2011
Loeb 1998
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Firenze 2011
The Sandage effect
sec/1|1
))(
1(
)(
)(
)(
)(
1
0
00
000
cmz
zcv
H
zHztHz
ta
ta
tta
ttaz
yr
sss
Corasaniti, Huterer, Melchiorri 2007
Balbi & Quercellini 2007
sec/3010
)10(10
9
9
0
cmc
yrstH
Euclid range
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Firenze 2011
EELT
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Firenze 2011
2010
CODEX at EELT
today... ...ten years later
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Firenze 2011
CODEX at EELT
Liske et al. 2008
scmzNNS QSO
/1
530
/
23502
8.12/1
• large colleting area • high resolution spetrographs • stable, low-peculiar motion targets: Lyman-alpha lines
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Firenze 2011
Two null cones are better than one!
1z
0z
now
VOID
time
com. dist. ttnow
inHoutH
Two null cones are better than one!
M. Quartin & L. A. 2009
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Firenze 2011 LTB void model, XXI century
Evolution
Us
Rest of the Universe
Ptolemaic system, I century
Us
Rest of the Universe
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Firenze 2011
Quercellini, Quartin & LA, Phys. Rev. Lett. 2009 arXiv 0809.3675
LTB void model
Cosmic Parallax
asrad
tH
20010
10
9
9
0
astrometric satellites GAIA, SIM, Jasmine etc: 1-100 µas
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Firenze 2011
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Firenze 2011
LTB void model
Garcia-Bellido & Haugbolle 2008
LTB models
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Firenze 2011
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Firenze 2011
Quercellini, Quartin & LA, arXiv 0809.3675
Garcia-Bellido & Haugbolle 2008
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Firenze 2011
Quercellini, Quartin & LA, arXiv 0809.3675
Cosmic Parallax
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Firenze 2011
Gaia: Complete, Faint, Accurate
Hipparcos Gaia
Magnitude limit 12 20 mag
Completeness 7.3 – 9.0 20 mag
Bright limit 0 6 mag
Number of objects 120 000 26 million to V = 15
250 million to V = 18
1000 million to V = 20
Effective distance limit
1 kpc 50 kpc
Quasars None 5 x 105
Galaxies None 106 – 10
7
Accuracy 1 milliarcsec 7 µarcsec at V = 10
10-25 µarcsec at V = 15
300 µarcsec at V = 20
Photometry photometry
2-colour (B and V) Low-res. spectra to V = 20
Radial velocity None 15 km/s to V = 16-17
Observing programme
Pre-selected Complete and unbiased
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Firenze 2011
Quercellini, Quartin & LA, arXiv 0809.3675
Garcia-Bellido & Haugbolle 2008
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Firenze 2011
Quercellini, Quartin & LA, arXiv 0809.3675
Garcia-Bellido & Haugbolle 2008
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Firenze 2011
Bianchi I
Not only LTB
a(t)
b(t)
c(t)
12
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Firenze 2011
Current limits on anisotropy
410
H
HR at z = 1000
810
H
Hat z = 0 in a ΛCDM universe
?
H
Hat z = 0 in anisotropic dark energy
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Firenze 2011
Anisotropic dark energy
DE
zanyatH
HR ,10 4
Mota & Koivisto 2008,
Barrow, Saha, Bruni, Rodrigues and many others..
C. Quercellini, P. Cabella, L.A.,
M. Quartin, A. Balbi 2009
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Firenze 2011
Precision is nothing without accuracy
The power of statistics
Lensing and supernovae
Homogeneity and isotropy
Growth factor AND bias to 2-3% in every
redshift bin.
Lensing effects are non-Gaussian and
cosmology dependent.
They can alter significantly the parameter
estimates.
Radial inhomogeneities and departures from
isotropy are not yet ruled out. Their existence
should be disproven or confirmed with next
generation experiments.
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Firenze 2011
Cambridge
University Press
2010
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Firenze 2011
Generalized density/velocity
Standard relation '
',
v
f f
F Generalized relation