What is the Fisher information content of cosmic shear surveys? - - PowerPoint PPT Presentation

SLIDE 1

What is the Fisher information content of cosmic shear surveys?

Olivier DorÉ,

JPL/Caltech

with Tingting Lu and Ue-Li Pen

arXiv:0905.0501

SLIDE 2

An old question

It a simple question, and we know how to answer if from an information theory point of view It is usually quantified through the Fisher Information (1936). For a random variables X, i.e. an observable, and some parameters p, it writes as It is now common wisdom for astrophysicists and widely used, e.g. to make cosmological parameter forecast

Inf =

• αβ

Fαβ Fαβ =

• ij

∂Xi ∂pα XT X−1

ij

∂Xi ∂pβ

A good question to ask, is what is the information content of cosmic shear survey, from an information theory point of view. It is not a new question of course, and we know the answer. We know how to formalize that, for example through the Fisher information, and it has been well studied to make fore

SLIDE 3

“surprising” answer for P(k)

What matters is not the absolute value but rather the scaling as compared with a Gaussian It can be shown that for a gaussian, Inf=#k modes The saturation is due to non-gaussian effects coming from the non-linear evolution of the density field Shown here for the amplitude only but true for other parameters too

Rimes & Hamilton 2006 Neyrinck et al. 06 O.D., Lu & Pen 09

Using 400 P3M sims (256 h/Mpc)3, 2563 part z=1

Inf =

• ij
• P(ki)P(kj)T −1

¯ P(ki) ¯ P(kj)

SLIDE 4

Halo Model insights

Fluctuations of the 1 halo term at trans-linear scale dominate the variance This contribution comes from rare and massive halo that induces a big shot noise This extra variance entails the lack of information

Neyrinck et al. 06

1 halo term 2 halo term

SLIDE 5

Lensing Convergence CL

Using 300 P3M sims, (1024 h/Mpc)3, 2563 part This quantity is important to optimize coming surveys Again, it can be shown that for a gaussian, Inf=#modes We expect non-gaussian effects to be milder due to projection effects Good convergence due to a new way to compute the covariance matrix from simulations O.D., T. Lu, U.-L. Pen 2009

Inf =

• ij
• Cκa

ℓi Cκb ℓj T −1

¯ Cκa

ℓi ¯

Cκb

ℓj

1 redshift bin 1<z<1.5 4 redshift bins 1<z<3

SLIDE 6

What consequences for cosmological information?

O.D., T. Lu, U.-L. Pen 2009

Effect potentially important, i.e. a factor of 4 for the DE FoM at high l But the effect is hidden by shot noise, at most a factor of 1.5

200 sq. deg. 1 z bin 5000 sq. deg. 3 z bins 200 sq. deg. 3 z bins 20000 sq. deg. 4 z bins

SLIDE 7

CMB Lensing

Milder saturation effect Sensitivity to higher z

O.D., T. Lu, U.-L. Pen 2009

SLIDE 8

Errors on the Errors

We claim an error on the errors of only 14% We develop an original scheme to compute the covariance matrix which offers a much better convergence We can improve the accuracy of the evaluation by an order of magnitude using only of a few times more simulations than previous works

O.D., T. Lu, U.-L. Pen 2009

SLIDE 9

Conclusions

We studied the non-linear contributions to the covariance matrix of convergence power spectra using N-body simulations Using a novel technique to compute the covariance matrix, we improve the convergence of the covariance matrix by an order

• f magnitude with only a factor few more sims

We reproduce previous results in the literature concerning the saturation of Fisher information at 3D We observe a similar effect at 2D although a less severe one due to projection effects Although the effects of non-linearities could degrade the FoM by a factor of ~4 when there is no shot noise, we find that realistic levels of shot noise mitigates this effect and the degradation is ~1.5 Making statistics of log(κ) instead of κ might help Consider only the 2 points information here

SLIDE 10

FIN

SLIDE 11

Saturation for other cosmological parameters

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Neyrinck et Szapudi 06