Exploitation of the gravitational lensing signal:

Probing the large scale structures with the CMB

Laurence Perotto; LAL Orsay BPol workshop

Laurence Perotto BPol workshopMotivations Method Prospects

The CMB lensing effect

n

n + d

d = the gravitational potential integrated along the line-of-sight

z~1100

z~1 to 3

z=0

From CMB maps, gravitational potential can be statistically reconstructed

Lensing effect introduces NG in the CMB maps in the form of:

mode couplingobservable correlation (e. g. EB, TB, etc. )

Motivations

Laurence Perotto BPol workshopMotivations Method Prospects

Free-streaming suppression

With lensing extraction, CMB data alone become sensitive to m , w , …

• no light-to-mass bias • probing high redshift structures: still in their linear regime• no need to a dedicated experiment

An alternative and advantageous measure of the matter density.

ν DE

Probing neutrino masses, dark energy, …

advantages:

Motivations

Laurence Perotto BPol workshopMotivations Method Prospects

Breaking cosmological parameters degeneracy : the Planck example

2 sensitivity to Mv of 0.3 eV

f = Ω/Ωdm

projected 68% and 95% C. L. within an 11-parameters Λ(H+C)DM model

2 sensitivity to Mv of 1 eV

without lensing

with with lensinglensing

LP, J. Lesgourgues, S. Hannestadt, H. Tu, Y. Wong [astro-ph/06062271]

Motivations

Laurence Perotto BPol workshopMotivations Method Prospects

Where is the lensing information?

both large and small scales are needed

dd

TT

EE

BB (T/S~0)r.m.s. of the

deflection angle:

~ 1 arcmin

correlation length:

~ few degrees

Method

Laurence Perotto BPol workshopMotivations Method Prospects

Full sky quadratic estimators methodW. Hu et T. Okamoto (2002)

a , b = { T, E, B }

geometrical coefficients

^

How to construct an estimator for the deflection?

∞

A 4-points estimator of the deflection field APS:

(ab) = TT, TE, TB, EE, EB

cosmic variance + instrumental noise

weighted sum over multipole pairs of observed modes

Method

Laurence Perotto BPol workshopMotivations Method Prospects

Noise spectra of quadratic estimators

Cl

dd

EBEB

TTTT

all combined

Nl

aba’b’ P ~ √2 K.arcminFWHM ~ 4 arcmin

« lensing designed »

Prospects

J. Lesgourgues, L. P., S. Pastor, M. Piat [ Phys. Rev. D (2006)]

Laurence Perotto BPol workshopMotivations Method Prospects

Can be calculated for any experiment…

EBEB

all combined

Nl

aba’b’

P = 6 K.arcminFWHM ~ 30 arcmin « SAMPAN-like »

J. Lesgourgues, L. P., S. Pastor, M. Piat [ Phys. Rev. D (2006)]

Prospects

Laurence Perotto BPol workshopMotivations Method Prospects

Lensing extraction with forthcoming experiments

Y Y Y

Y = { T, E, d }

Y Y Y

Y = { T, E, d }

« ideal »

Prospects

Laurence Perotto BPol workshopMotivations Method Prospects

Is this feasible in «real world»?

Lots of noises and secondaries could mimic the lensing signature…

the systematics:

sky cutnon-axisymetric beam

…

generate an E to B leakage

kinetic SZ effect

the foregrounds:

( A. Amblard et al. [astro-ph/06062271] )

point sources ( LP thesis [tel-00011916] )

polarized dust

…

tests of the robustness of the estimator against foregrounds and systematics residuals are needed

Prospects

Laurence Perotto BPol workshopMotivations Method Prospects

Exploiting CMB lensing

A powerfull tool to probe LSS

constraining m_nu, w_de, …breaking parameters degeneracy

Lensing extraction requires both small and large angular scales

ideal CMB lensing experiment should provide high quality full sky E and B-mode maps with ~arcmin resolution.

However, lensing extraction on a low-resolution SAMPAN-like experiment in combination to Planck would provide high added value

A quadratic estimator method should be sufficient

but tests of the robustess against foregrounds and systematics residuals are needed

Laurence Perotto BPol workshopMotivations Method Prospects

Probing the matter distribution with Planck

Prospects

J. Lesgourgues, L. P., S. Pastor, M. Piat [ Phys. Rev. D (2006)]

The expected error on angular power spectra reconstruction:

TT

EE

dd

BB

multipole l

angular scale90° 2° 0.2°

E-mode(curl-free)

B-mode(gradient-free)

Temperature

deflection angles field

Laurence Perotto BPol workshopMotivations Method Prospects

How to probe neutrino mass in Cosmology?

Probes

The clearer signature of massive neutrinos: the free-streaming effect

Gravitationnal collapse

in an expanding Universe

baryons+CDM

neutrinos

Neutrinos cannot collapse below a diffusion lenght:

= ∫ v dt

For (2/k) < , free-streaming supresses growth of structures.

Laurence Perotto BPol workshopMotivations Method Prospects

quadratic estimators sensitivity

Cl

dd

EBEB

TTTTcombiné

Nl

Laurence Perotto BPol workshopMotivations Method Prospects

Lensing extraction with up-coming experiments

Y Y Y

Y = { T, E, d }

Laurence Perotto BPol workshopMotivations Method Prospects

Is it sufficient?

P = √2 K.arcminFWHM = 4 arcmin

C. Hirata & U. Seljak [astro-ph/0306354]

Laurence Perotto BPol workshopMotivations Method Prospects

masse totale (eV)0.06 0.1

NH IH

Probing neutrino mass with CMB lensing

dTT

dEB

Inflation Probe/ Cosmic Vision WMAP+SDSS

1

Forecasts on several up-coming exp. sensitivity in eV

0.2

PlanckSAMPAN

Planck

0.3

Laurence Perotto BPol workshopMotivations Method Prospects

Lensing extraction with up-coming experiments

Y Y Y

Y = { T, E, d }

Laurence Perotto BPol workshopMotivations Method Prospects

Laurence Perotto BPol workshopMotivations Method Prospects