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ÅÅrhus, 4rhus, 4 September September 2007 2007
Julien Lesgourgues (LAPTHJulien Lesgourgues (LAPTH, Annecy, France, Annecy, France))
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Structure formationStructure formation
m + H m = 4G mm
expansion gravitational forces
3H2=8G i ii
linear growth factor
for CDM : cdm, b cdm, b cdm a
(MD)
for MDM, large scales : cdm, b, cdm, b, cdm
a
“ “ , small scales : cdm, b, cdm, b cdm
a1-3/5 f
.. ....
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Structure formationStructure formation
m + H m = 4G mm
expansion gravitational forces
3H2=8G i ii
linear growth factor
for CDM : cdm, b cdm, b cdm a
(MD)
for MDM, large scales : cdm, b, cdm, b, cdm
a
“ “ , small scales : cdm, b, cdm, b cdm
a1-3/5 f
.. ....
smaller than
free-streaming scale
FS = a(t) ∫ <v> dt/a
signature of free-streaming
f = / m ≈ (m)/(15 eV)
Bond, Efstathiou & Silk 1980
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cdm
b
metric
a
J.L.
& S
. Past
or,
Physi
cs R
eport
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60
34
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]J.L.
& S
. Past
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Physi
cs R
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stro
-ph/0
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Free-streaming and structure Free-streaming and structure formationformation
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cdm
b
metric
a
1-3/5fa
J.L.
& S
. Past
or,
Physi
cs R
eport
s [a
stro
-ph/0
60
34
94
]J.L.
& S
. Past
or,
Physi
cs R
eport
s [a
stro
-ph/0
60
34
94
]
Free-streaming and structure Free-streaming and structure formationformation
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accélération
accélération
décélération lente
décélération rqpide
accélération
accélération
décélération lente
décélération rqpide
inflation radiation matière énergie noire
??
Why is the signature of Why is the signature of
massive neutrinos massive neutrinos
non-degenerate with non-degenerate with
other cosmological other cosmological
parameters?parameters?
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A. characteristic shape of matter power spectrum today
Why is the signature of massive Why is the signature of massive neutrinos non-degenerate with other neutrinos non-degenerate with other
cosmological parameters?cosmological parameters?
P(k) = m2
kk
Light neutrinos step-like suppression
-8f-8f (from 3% to 60% (from 3% to 60% for 0.05eV to 1eV)for 0.05eV to 1eV)
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A. characteristic shape of matter power spectrum today
Why is the signature of massive Why is the signature of massive neutrinos non-degenerate with other neutrinos non-degenerate with other
cosmological parameters?cosmological parameters?
PP
kk
Light neutrinos step-like suppression
dark energy
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A. characteristic shape of matter power spectrum today
Why is the signature of massive Why is the signature of massive neutrinos non-degenerate with other neutrinos non-degenerate with other
cosmological parameters?cosmological parameters?
PP
kk
Light neutrinos step-like suppression
primordial tilt
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A. characteristic shape of matter power spectrum today
Why is the signature of massive Why is the signature of massive neutrinos non-degenerate with other neutrinos non-degenerate with other
cosmological parameters?cosmological parameters?
PP
kk
Light neutrinos step-like suppression
primordial tilt
tilt running
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B. linear growth factor
Why is the signature of massive Why is the signature of massive neutrinos non-degenerate with other neutrinos non-degenerate with other
cosmological parameters?cosmological parameters?
P(k,a)/aP(k,a)/a22
==(1+z(1+z22) P(k,z)) P(k,z)
kk
sCDM no linear growth factor
sCDM (no DE, no msCDM (no DE, no m))
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B. linear growth factor
Why is the signature of massive Why is the signature of massive neutrinos non-degenerate with other neutrinos non-degenerate with other
cosmological parameters?cosmological parameters?
P(k,a)/aP(k,a)/a22
==(1+z(1+z22) P(k,z)) P(k,z)
kk
DE+CDM scale-independent linear growth factor
sCDM (no DE, no msCDM (no DE, no m))
DE+CDM (no mDE+CDM (no m))
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B. linear growth factor
Why is the signature of massive Why is the signature of massive neutrinos non-degenerate with other neutrinos non-degenerate with other
cosmological parameters?cosmological parameters?
P(k,a)/aP(k,a)/a22
==(1+z(1+z22) P(k,z)) P(k,z)
kk
DE+CDM+m scale-dependent linear growth factor
sCDM (no DE, no msCDM (no DE, no m))
DE+CDM+HDMDE+CDM+HDM
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B. linear growth factor
Why is the signature of massive Why is the signature of massive neutrinos non-degenerate with other neutrinos non-degenerate with other
cosmological parameters?cosmological parameters?
Large scale:Large scale:
D(z) = cst during MD, non-trivial during DED;D(z) = cst during MD, non-trivial during DED;
Small scale:Small scale:
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Conclusion:
For precise enough data, the
effect of neutrino masses on
CMB and LSS is clearly non-
degenerate with that of any
other ingredient
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Current & future methods for Current & future methods for detecting neutrino masses with detecting neutrino masses with cosmological perturbation theorycosmological perturbation theory
CMB (primary temperature anisotropies) CMB (primary temperature anisotropies)
LaurenceLaurence
galaxy/cluster redshift surveys galaxy/cluster redshift surveys OferOfer
galaxy weak lensing (cosmic shear surveys) galaxy weak lensing (cosmic shear surveys) YvonneYvonne
CMB weak lensing (CMB lensing extraction) CMB weak lensing (CMB lensing extraction) LaurenceLaurence
quasar spectra (Lyman-alpha forests)quasar spectra (Lyman-alpha forests)
cluster countingcluster counting
ISW effectISW effect
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Possible probes of Possible probes of linear growth factor ?linear growth factor ?
Direct study of dependence of LSS 2-point Direct study of dependence of LSS 2-point correlation function w.r.t z, using:correlation function w.r.t z, using:
galaxy overdensitygalaxy overdensity
cosmic shearcosmic shear
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PP
kk
-8f-8f (from 3% to 60% (from 3% to 60% for 0.05eV to 1eV)for 0.05eV to 1eV)
Galaxy redhsift surveysGalaxy redhsift surveysCurrent:Current:2dF, SDSS2dF, SDSS
Future:Future:SDSS-II, -III, cluster surveys …SDSS-II, -III, cluster surveys …
… … possible to cut in redshift bins!possible to cut in redshift bins!
probes this regionprobes this region
biasnon-linearevolution
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Weak lensing: galaxy Weak lensing: galaxy shearshear
Future:Future:many dedicated many dedicated surveys surveys (CFHTLS, DES, SNAP, (CFHTLS, DES, SNAP, Pan-STARRS, LSST, Pan-STARRS, LSST, Dune, …)Dune, …)
Map of gravitational potentialMap of gravitational potentialprojected along line-of-sightprojected along line-of-sight
COSMOSCOSMOS
Massey et al., Nature 05497, 7 january 2007Massey et al., Nature 05497, 7 january 2007
tomographtomographyy
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Weak lensing: galaxy Weak lensing: galaxy shearshear
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CMB and late ISWCMB and late ISW
Primary CMB anisotropies not Primary CMB anisotropies not
very sensitive to neutrino very sensitive to neutrino
masses, masses,
but various secondary effects but various secondary effects
sensitive to LSS:sensitive to LSS:- weak lensing weak lensing (Laurence’s (Laurence’s
talk)talk)- Sunayev Zel’dovitch effectSunayev Zel’dovitch effect- late integrated Sachs Wolfelate integrated Sachs Wolfe
CMB photon
gravitational potential
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Late ISW and neutrino Late ISW and neutrino massmass
CMB photon
gravitational potential
Poisson: (k2/a2) = 4G mm
Massless neutrinos, MD: = cst
varies: - due to DE on all scales, small z - due to f on small scales, all z
late ISWlate ISW
What is the effect of mWhat is the effect of m? Suppression, or boost induced by ISW? ? Suppression, or boost induced by ISW?
Valkenburg, JL & Gaztanaga, in prep.Valkenburg, JL & Gaztanaga, in prep.
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CMB and late ISWCMB and late ISW
Effect of fEffect of f : :
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CMB and late ISWCMB and late ISW
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CMB and late ISWCMB and late ISW
Ideal experiment:Ideal experiment:
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CMB and late ISWCMB and late ISW
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CMB and late ISWCMB and late ISW
Ideal experiment:Ideal experiment:
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CMB and late ISWCMB and late ISW
Detailed error forecast for Planck + LSSTDetailed error forecast for Planck + LSST
Well-known sensitivityWell-known sensitivity80 gal. / sq arcmin80 gal. / sq arcmin6 redshift bins6 redshift bins
Generate some mock data and fit it with Generate some mock data and fit it with 8-parameter model: 8-parameter model: CDM + mCDM + m+ w, using MCMC+ w, using MCMC
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CMB and late ISWCMB and late ISW
0.020 0.024