ÅÅrhus, 4rhus, 4 September September 2007 2007Julien Lesgourgues (LAPTHJulien Lesgourgues (LAPTH, Annecy, France, Annecy, France))

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

.. ....

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

cdm

b

metric

a

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Free-streaming and structure Free-streaming and structure formationformation

cdm

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a

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. & S

. Pas

tor,

Phys

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0603

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Free-streaming and structure Free-streaming and structure formationformation

accélération

accélérationdécélération lente

décélération rqpide

accélération

accélérationdécélération 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?

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)

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

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

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

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))

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))

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

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:

Conclusion:

For precise enough data, the effect of neutrino masses on CMB and LSS is clearly non-degenerate with that of any

other ingredient

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

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

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

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

Weak lensing: galaxy Weak lensing: galaxy shearshear

CMB and late ISWCMB and late ISWPrimary 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

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.

CMB and late ISWCMB and late ISW

Effect of fEffect of f : :

CMB and late ISWCMB and late ISW

CMB and late ISWCMB and late ISW

Ideal experiment:Ideal experiment:

CMB and late ISWCMB and late ISW

CMB and late ISWCMB and late ISW

Ideal experiment:Ideal experiment:

CMB and late ISWCMB and late ISWDetailed error forecast for Planck + LSSTDetailed error forecast for Planck + LSST

Well-known sensitivityWell-known sensitivity 80 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

CMB and late ISWCMB and late ISW

0.020 0.024