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

What is the Fisher information content of cosmic shear surveys? Olivier Dor É, JPL/Caltech with Tingting Lu and Ue-Li Pen arXiv:0905.0501

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 � Inf F αβ = αβ ∂ X i ∂ X i � X T X � − 1 � F αβ = ij ∂ p α ∂ p β ij It is now common wisdom for astrophysicists and widely used, e.g. to make cosmological parameter forecast 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

“surprising” answer for P(k) P ( k i ) P ( k j ) T � − 1 � � Inf = P ( k i ) ¯ ¯ P ( k j ) ij Using 400 P 3 M sims (256 h/Mpc) 3 , 256 3 part z=1 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

Halo Model insights 2 halo term 1 halo term 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

Lensing Convergence C L T � − 1 � C κ a ℓ i C κ b ℓ j � Inf = C κ a C κ b ¯ ℓ i ¯ ℓ j ij 1 redshift bin 1<z<1.5 4 redshift bins 1<z<3 Using 300 P3M sims, (1024 h/Mpc)3, 256 3 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

What consequences for cosmological information? 200 sq. deg. 200 sq. deg. 1 z bin 3 z bins 5000 sq. deg. 20000 sq. deg. 3 z bins 4 z bins 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 O.D., T. Lu, U.-L. Pen 2009

CMB Lensing Milder saturation effect Sensitivity to higher z O.D., T. Lu, U.-L. Pen 2009

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

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 of 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

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Saturation for other cosmological parameters 2 l n f l n � h l n A t i l t l n h b m 1 1 1 1 10 1 ) A 10 0 10 -1 n 10 -2 l ( � 10 -3 -1 -1 -1 -1 10 -1 10 0 10 1 10 2 1 1 1 ) 10 0 t l 10 -1 i t ( 10 -2 � 10 -3 -1 -1 -1 10 -1 10 0 10 1 10 2 1 1 ) 10 0 h 10 -1 n l 10 -2 ( 3 � 10 -3 -1 -1 V = ( 2 � / k ) m i n 10 -1 10 0 10 1 10 2 10 3 1 b ) l n A 10 0 f 10 2 t i l t 10 -1 n l n h l 10 -2 ( 10 1 l n f � 10 -3 b -1 2 10 -1 10 0 10 1 10 2 � l n � h m 10 0 ) 2 10 0 h M a r g i n a l i z e d m 10 -1 10 -1 � M a r g , h a l o f i t n 10 -2 U n m a r g i n a l i z e d l ( 10 -3 10 -2 � U n m a r g , h a l o f i t 10 -1 10 0 10 1 10 2 10 -2 10 -1 10 0 10 1 10 2 10 3 k = 1 0 k [ h / M p c ] k [ h / M p c ] m a x m a x m i n Neyrinck et Szapudi 06