The nature of Dark Energy · •Dark energy coupling •Early dark energy •Ultra-light fields...
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Firenze 2011 Luca Amendola ITP, University of Heidelberg Accuracy cosmology or, Testing DE with future surveys
Transcript of The nature of Dark Energy · •Dark energy coupling •Early dark energy •Ultra-light fields...
Firenze 2011
Luca Amendola
ITP, University of Heidelberg
Accuracy cosmology or, Testing DE with future surveys
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
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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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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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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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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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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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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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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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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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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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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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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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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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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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Present constraints on gamma
C. Di Porto & L.A. Phys.Rev. 2007
DGP
LCDM
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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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Euclid forecasts, I
Euclid current vs. Euclid
C. Di Porto, L.A., E. Branchini 2011
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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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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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Euclid forecasts, IV
Coupled dark energy
Effects on CMB, growth rate, BAO peaks, etc
growth
CMB
BAO
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Euclid forecasts, IV
Coupled dark energy
Put combined constraints
CMB+P(k)+WL
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Euclid forecasts, IV
Coupled dark energy
Combined constraint on coupling
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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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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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Lensing of distant sources
Marra & Kainulainen 2009
Lens parameters: Halo mass and concentration
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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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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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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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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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One null cone
0H
1z
0znow
time
comoving dist. 0H
z
zHa
1
)(
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One null cone
inH
1z
0znow
VOID
time
com. dist. outH
One null cone
z
rzHa
1
),(
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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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Sandage 1962
yearcmv sec//1
)( 1zH )( 2zH
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Loeb 1998
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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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EELT
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2010
CODEX at EELT
today... ...ten years later
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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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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
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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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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LTB void model
Garcia-Bellido & Haugbolle 2008
LTB models
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Quercellini, Quartin & LA, arXiv 0809.3675
Garcia-Bellido & Haugbolle 2008
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Quercellini, Quartin & LA, arXiv 0809.3675
Cosmic Parallax
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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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Quercellini, Quartin & LA, arXiv 0809.3675
Garcia-Bellido & Haugbolle 2008
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Quercellini, Quartin & LA, arXiv 0809.3675
Garcia-Bellido & Haugbolle 2008
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Bianchi I
Not only LTB
a(t)
b(t)
c(t)
12
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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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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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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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Cambridge
University Press
2010
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Generalized density/velocity
Standard relation '
',
v
f f
F Generalized relation
