1. Laurence Perotto; LAL Orsay
Exploitation of the gravitational lensing signal: Probing the large scale structures with the CMB
my presentation is about the sensitivity of Cosmology to the neutrino masses, using the weak lensing effect on the cosmic microwave background. I give the bounds on the neutrino masses the future experiments like Planck satellite and beyond.
Laurence Perotto; LAL Orsay
BPol workshop

2. The CMB lensing effect n + d d = F
z~1 to 3
z=0
d = F
F: the gravitational potential integrated along the line-of-sight
z~1100
Lensing effect introduces NG in the CMB maps in the form of:
mode coupling
- The CMB photon geodesic are incurved/deflected by gravitational potential of the strutures in the line-of-sight.
- the consequences is a remapping of the CMB maps by small deflection angles. the deflection equals the gradient of phi: the line-of sight projection of the gravitational potential.
The lensing effect introduce some NG in the CMB maps in the form of:
- different modes of a same CMB observable become correlated
- new correlation between different observable appears
- Using these specific signature in the CMB maps , it’s possible to statiscally reconstruct the gravitational potentiel of the subjacent matter.
(So CMB lensing allows to probe the LSS from the Last scattering surface of the CMB photons (z~1000) to us with a maximum efficiency near z~1-3. )
observable correlation (e. g. EB, TB, etc. )
From CMB maps,
gravitational potential can be statistically reconstructed
Motivations

3. Probing neutrino masses, dark energy, …
Free-streaming
suppression
An alternative and advantageous measure of the matter density.
advantages:
no light-to-mass bias
probing high redshift structures: still in their linear regime
no need to a dedicated experiment
(Lensing effect is not only a source of confusion for the primordial CMB signal, it’s also a powerfull tool to probe the large scale structures: )
Lensing signal provides an alternative and etc.
Thus, Lensing signal can be used to constrain anycosmological par. which affect the shape of the P(k).
Here, as an example I show the effect of a non-zero total neutrino mass on P(k)
Thus, Thanks to lensing extraction CMB data etc.
With lensing extraction,
CMB data alone become sensitive to m , w , … ν DE
Motivations

4. Breaking cosmological parameters degeneracy : the Planck example
projected 68% and 95% C. L. within an 11-parameters Λ(H+C)DM model
without lensing
2s sensitivity to Mv of 1 eV
with lensing
fn = Ωn /Ωdm
2s sensitivity to Mv of 0.3 eV
titre : Lensing extraction also helps to break the cosmo par…
here I give an example of such a breaking for the Planck exp.
The plot shows the projected 68% and 95% confidence levels on two parameters : the fraction of dark matter in the form of neutrinos versus the dark matter density.
In blue the contours are calculated with CMB but without any lensing extraction.
The coloured shape are the contours obtained when lensing signal is added.
Thus, lensing information allows a better constrain of the parameters.
(The contours have been calulated from a MCMC analysis within an 11-par Hot+Cold dark matter model.)
LP, J. Lesgourgues, S. Hannestadt, H. Tu, Y. Wong [astro-ph/ ]
Motivations

5. Where is the lensing information?dd TT EE
BB (T/S~0)
correlation length:
~ few degrees
r.m.s. of the deflection angle:
- here I assess the question: which range of scale should be measured to perform a lensing extraction?
In the plot, I show: in green the deflection power spectrum and in red, the lensed power spectra of the CMB for T,E-mode and B-mode
in one hand, the lensed CMB spectra are smoothed mainly at the small scale: the rms etc.
in the other hand, the deflection field responsible of such an effect has a maximun of power at large scale; as a consequences, the deflection angles are correlated over few degrees scales.
so for lensing extraction, both large etc.
~ 1 arcmin
both large and small scales are needed
Method

6. Full sky quadratic estimators method
W. Hu et T. Okamoto (2002)
a , b = { T, E, B }
geometrical coefficients
How to construct an estimator for the deflection? ^
weighted sum over multipole pairs of observed modes
(ab) = TT, TE, TB, EE, EB
A 4-points estimator of the deflection field APS:
cosmic variance + instrumental noise
Method

7. Noise spectra of quadratic estimators
P ~ √2 K.arcmin
FWHM ~ 4 arcmin
« lensing designed » N l
aba’b’ C l dd
TTTT
EBEB
all combined
J. Lesgourgues, L. P., S. Pastor, M. Piat [ Phys. Rev. D (2006)]
Prospects

8. Can be calculated for any experiment…
aba’b’
EBEB
all combined
P = 6 K.arcmin
FWHM ~ 30 arcmin
« SAMPAN-like »
J. Lesgourgues, L. P., S. Pastor, M. Piat [ Phys. Rev. D (2006)]
Prospects

9. Lensing extraction with forthcoming experimentsY
Y = { T, E, d }
« ideal »
transition: all the calculations I have shown were performed assuming the very cleaned CMB maps. Now I will assess an open question… Y
Y = { T, E, d }
Prospects

10. Is this feasible in «real world»?
Lots of noises and secondaries could mimic the lensing signature…
the systematics:
sky cut
non-axisymetric beam
generate an E to B leakage …
the foregrounds:
kinetic SZ effect
( A. Amblard et al. [astro-ph/ ] )
point sources
( LP thesis [tel ] )
polarized dust …
tests of the robustness of the estimator against foregrounds and systematics residuals are needed
Prospects

11. 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

12. Probing the matter distribution with Planck
The expected error on angular power spectra reconstruction:
angular scale
90° 2°
0.2° dd
deflection angles field TT
Temperature
E-mode
(curl-free) EE
here I show the expected binned 1 sigma error on the reconstruction of the angular power spectra. (contains the same information than the power spectrum but for some fields on the sphere insteads of on a plane)
one can see :
1/ red: deflection angles field
2/blue: temperature of CMB anisotropies
3/ the two others are the spectra of the polarisation of the CMB anosotropies. One use to decompose the linear polarisation of the CMB in two different field the so-called E_mode (or curl-free) and B-mode (or gradient-free).
Thanks to lensing extraction, Planck could lead to resonably good measure of the structures in a range of scale sensitive to the free-streaming effect of the neutrinos thus sensitive to the neutrino masses. BB
B-mode
(gradient-free)
multipole l
J. Lesgourgues, L. P., S. Pastor, M. Piat [ Phys. Rev. D (2006)]
Prospects

13. How to probe neutrino mass in Cosmology?
The clearer signature of massive neutrinos: the free-streaming effect
Neutrinos cannot collapse below a diffusion lenght:
l = ∫ v dt
Gravitationnal
collapse
in an
expanding Universe
First, since neutrinos contribute to the energy budget of the Universe, they also contribute to its homogeneous expansion. Any cosmological probes, such as CMB, should be sensitive to neutrinos. But this background effect on the cosmological data is very weak (< 1%) .
The main signature of neutrino mass arises from their free-streaming effect, which affects the growth of the large scale structures.
here I have an illustration of this effect.
(The LSS in the Universe formed during the matter domination epoch by gravitationnal collapse.)
1/ First without any neutrino:The orange circles represent the baryon and CDM: structures form by gravitational collapse in an expanding Universe.
2/ now if we add neutrinos (the blue-filled circles). Because of their hight speed dispersion, they can escape from the smallest structures; They can’t cluster bellow a given scale: their diffusion length, depending on their mass.
The neutrinos contribute to the homogenous expansion of the Universe (which tend to dilute the structures) without contributing to the gravitational clustering (leading effect of the structure formation)
The resulting effect is to slow down the growth of the structure smaller than the neutrinos diffusion length.
Thus the cosmological probes of the neutrinos mass are the experiments measuring the LSS.
baryons+CDM
For (2p/k) < l ,
free-streaming supresses growth of structures.
neutrinos
Probes

14. quadratic estimators sensitivityl dd
EBEB
TTTT
combiné N 

15. Lensing extraction with up-coming experimentsY
Y = { T, E, d }

16. Is it sufficient? FWHM = 4 arcmin P = √2 K.arcmin
C. Hirata & U. Seljak [astro-ph/ ]

17. Probing neutrino mass with CMB lensing
Forecasts on several up-coming exp. sensitivity in eV d TT d EB
Inflation Probe/ Cosmic Vision
masse totale (eV)
0.06
0.1 NH IH
0.2
Planck
SAMPAN
Planck
0.3
WMAP+SDSS 1

18. Lensing extraction with up-coming experimentsY
Y = { T, E, d }