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Weak Lensing Tomography Sarah Bridle University College London

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3d vs 2d (tomography) Non-Gaussian -> higher order statistics Low redshift -> dark energy versus

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Weak Lensing Tomography 1.In principle (perfect zs) Hu 1999 astro-ph/ Photometric redshifts Csabai et al. astro-ph/ Effect of photometric redshift uncertainties Ma, Hu & Huterer astro-ph/ Intrinsic alignments 5.Shear calibration

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1. In principle (perfect zs) Qualitative overview Lensing efficiency and power spectrum –Dependence on cosmology Power spectrum uncertainties Cosmological parameter constraints

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1. In principle (perfect zs) Core reference Hu 1999 astro-ph/ See also Refregier et al astro-ph/ Takada & Jain astro-ph/

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Cosmic shear two point tomography

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(Hu 1999)

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Lensing efficiency (Hu 1999) Equivalently: g i (z l ) = ∫ z l n i (z s ) D l D ls / D s dz s i.e. g is just the weighted D l D ls / D s

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Can you sketch g 1 (z) and g 2 (z)? (Hu 1999) g i (z) = ∫ z s n i (z s ) D l D ls / D s dz s

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Lensing efficiency for source plane?

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(Hu 1999)

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Sensitivity in each z bin

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NOT

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(Hu 1999) Why is g for bin 2 higher? A. More structure along line of sight B. Distances are larger g i (z d ) = ∫ z s 1 n i (z s ) D d D ds / D s dz s

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* *

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Lensing power spectrum (Hu 1999)

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Lensing power spectrum Equivalently: P ii (l) = ∫ g i (z l ) 2 P(l/D l,z) dD l /D l 2 i.e. matter power spectrum at each z, weighted by square of lensing efficiency (Hu 1999)

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Measurement uncertainties 1/2 = rms shear (intrinsic + photon noise) n i = number of galaxies per steradian in bin i (Hu 1999) Cosmic Variance Observational noise

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(Hu 1999)

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Sensitivity in each z bin

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NOT

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(Hu 1999)

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Dependence on cosmology Refregier et al SNAP3 ?? A. m = 0.35 w=-1 B. m = 0.30 w=-0.7

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Approximate dependence Increase 8 → A. P ↓ B. P ↑ Increase z s → A. P ↓ B. P ↑ Increase m → A. P ↓ B. P ↑ Increase DE ( K =0) → A. P ↓ B. P ↑ Increase w → A. P ↓ B. P ↑ Huterer et al

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Effect of increasing w on P Distance to z –A. Decreases B. Increases

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Perlmutter et al.1998 Fainter Further away Decelerating Accelerating m =1, no DE m =1, DE =0) == ( m = 0.3, DE = 0.7, w DE =0)

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Perlmutter et al.1998 EdS OR w=0 w=-1 Fainter, further Brighter, closer

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Effect of increasing w on P Distance to z –A. Decreases B. Increases –When decrease distance, lensing effect decreases Dark energy dominates –A. Earlier B. Later

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Effect of increasing w on P Distance to z –A. Decreases B. Increases –When decrease distance, lensing decreases Dark energy dominates –A. Earlier B. Later Growth of structure –A. Suppressed B. Increased –Lensing A. Increases B. Decreases Net effects: –Partial cancellation decreased sensitivity –Distance wins

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Approximate dependence Increase 8 → A. P ↓ B. P ↑ Increase z s → A. P ↓ B. P ↑ Increase m → A. P ↓ B. P ↑ Increase DE ( K =0) → A. P ↓ B. P ↑ Increase w → A. P ↓ B. P ↑ Huterer et al

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Approximate dependence Increase 8 → A. P ↓ B. P ↑ Increase z s → A. P ↓ B. P ↑ Increase m → A. P ↓ B. P ↑ Increase DE ( K =0) → A. P ↓ B. P ↑ Increase w → A. P ↓ B. P ↑ Huterer et al Note modulus

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Which is more important? Distance or growth? Simpson & Bridle

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Dependence on cosmology Refregier et al SNAP3 ?? A. m = 0.35 w=-1 B. m = 0.30 w=-0.7

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(Hu 1999)

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See Heavens astro-ph/ for full 3D treatment (~infinite # bins)

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(Hu 1999)

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Parameter estimation for z~2 (Hu 1999)

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Predict the direction of degeneracy in w versus m plane

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Refregier et al SNAP3

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(Hu 1999)

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Takada & Jain

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(Hu 1999)

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Covariance matrix P 12 is correlated with P 11 and P 22 (ignoring trispectrum contributions) Takada & Jain

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How many redshift bins to use? Ma, Hu & Huterer 5 is enough Modified from

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Higher order statistics

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Takada & Jain

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Geometric information Jain & Taylor; Kitching et al. Slide stolen from Tom Kitching

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Slide stolen from presentation by Andy Taylor

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Slide stolen from presentation by Andy Taylor

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Slide stolen from presentation by Andy Taylor

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Slide stolen from presentation by Andy Taylor

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Some additional tomographic methods Cross-correlation cosmography –Bernstein & Jain astro-ph/ Galaxy-lensing cross correlation –Hu & Jain astro-ph/ Reconstruction of distance and growth –Song; Knox & Song

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