Weak Lensing Tomography Sarah Bridle University College London

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

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

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

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

Cosmic shear two point tomography  

 

  



(Hu 1999)

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

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

Lensing efficiency for source plane?

(Hu 1999)

Sensitivity in each z bin

NOT

(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

* *

Lensing power spectrum (Hu 1999)

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)

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

(Hu 1999)

Sensitivity in each z bin

NOT

(Hu 1999)

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

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

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

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)

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

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

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

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

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

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

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

(Hu 1999)

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

(Hu 1999)

Parameter estimation for z~2 (Hu 1999)

Predict the direction of degeneracy in w versus  m plane

Refregier et al SNAP3

(Hu 1999)

Takada & Jain

(Hu 1999)

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

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

Higher order statistics

Takada & Jain

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

Slide stolen from presentation by Andy Taylor

Slide stolen from presentation by Andy Taylor

Slide stolen from presentation by Andy Taylor

Slide stolen from presentation by Andy Taylor

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