Dark Energy with 3D Dark Energy with 3D Cosmic ShearCosmic Shear

Alan HeavensAlan HeavensInstitute for Astronomy Institute for Astronomy

University of Edinburgh University of Edinburgh UK UK

with Tom Kitching, Patricia Castro, with Tom Kitching, Patricia Castro, Andy Taylor, Catherine Heymans et alAndy Taylor, Catherine Heymans et al

Bernard Jones. Valencia Bernard Jones. Valencia 30/06/0630/06/06

OutlineOutline

Dark Energy, Dark MatterDark Energy, Dark Matter Weak lensingWeak lensing 3D weak lensing3D weak lensing Statistical and Statistical and

systematics controlsystematics control First 3D resultsFirst 3D results from COMBO-17 from COMBO-17 FutureFuture

Bernard and lensingBernard and lensing

Major questionsMajor questions

What is the Dark Matter?What is the Dark Matter? What is the Dark Energy/What is the Dark Energy/ΛΛ??

TgG

gTG Scalar field? Quintessence:

Detection of w(z)Detection of w(z)

Effects of w: distance-redshift relation Effects of w: distance-redshift relation r(z),r(z), and growth and growth rate rate gg

Various methodsVarious methods Supernova Hubble diagram (Supernova Hubble diagram (DDLL)) Baryon wiggles (Baryon wiggles (DDAA)) Cluster abundance vs z (Cluster abundance vs z (gg)) 3D weak lensing (3D weak lensing (r(z),r(z), and and gg))

Probing bothProbing both r(z) r(z) andand g g may allow lifting of degeneracy may allow lifting of degeneracy between dark energy and modified gravity lawbetween dark energy and modified gravity law

3D weak lensing:3D weak lensing: physics well understood; needs physics well understood; needs excellent optical qualityexcellent optical quality

Gravitational LensingGravitational Lensing

Coherent distortion of Coherent distortion of background imagesbackground images

Shear, Magnification, Shear, Magnification, AmplificationAmplification

1

2

e.g. Gunn 1967 (Feynman 1964); Kristian & Sachs 1966 Complex shear =1 + i 2

βθ

Van Waerbeke & Mellier 2004

Shear, Dark Matter and CosmologyShear, Dark Matter and Cosmology

Lensing potential Lensing potential φφ

Lensing potential related to peculiar gravitational potential by

(Flat Universe)

Ellipticity of galaxy Ellipticity of galaxy e = e(intrinsic) + e = e(intrinsic) +

Cosmic shear: Cosmic shear: ~1% ~1% distortionsdistortions

Estimate Estimate by by averaging over many averaging over many galaxiesgalaxies

Estimating shearEstimating shear

E.g. Shear-shear correlations E.g. Shear-shear correlations on the skyon the sky Theoretically related to nonlinear matter power spectrumTheoretically related to nonlinear matter power spectrum

Need to know redshift distribution of sources – photo-zsNeed to know redshift distribution of sources – photo-zs

2D weak lensing2D weak lensing

3D nonlinear matter power spectrum

Number density of sources (photo-zs)

Peacock, Dodds 96;

Smith et al 2003

Simulated: Jain et al 2000

Recent results: CFHTLSRecent results: CFHTLS

Hoekstra et al 2005; see also Semboloni et al 2005

22 sq deg; median z=0.8

What are the fundamental What are the fundamental limitations?limitations?

Intrinsic alignments ?Intrinsic alignments ?• Lensing signal: coherent distortion of background images

• Lensing analysis assumes orientations of source galaxies are uncorrelated

• Intrinsic correlations destroy this

Weak lensing e = eI +

ee* = eIe*I + *

Intrinsic alignmentsIntrinsic alignments

Heavens, Refregier & Heymans 2000, Croft & Metzler 2000, Crittenden et al 2001 etc

Observations (SuperCOSMOS) Brown et al 2001

eIeI*: Theory: Tidal torquesTheory: Tidal torques

Downweight/discard pairs with similar photometric redshifts (Heymans & Heavens 2002; King & Schneider 2002a,b)

REMOVES EFFECT ~COMPLETELY

ee* = * + eIeI* + 2eI*

Efstathiou & Jones 1979Efstathiou & Jones 1979

1000 particle simulations1000 particle simulations

Shear-intrinsic alignments Shear-intrinsic alignments ‹‹eeγγ**››

Tidal field contributes to weak shear (of background)Tidal field contributes to weak shear (of background)

Tidal field could also orient galaxies (locally)Tidal field could also orient galaxies (locally) ((Hirata & Seljak Hirata & Seljak

20042004; Mandelbaum et al 2005, Trujillo et al 2006, Yang et al 2006); Mandelbaum et al 2005, Trujillo et al 2006, Yang et al 2006)

Expect 5-10% contamination

Theory: Heymans, AFH et al 2006SDSS: Mandelbaum et al 2005

Removing contaminationRemoving contamination

Intrinsic-intrinsic removal is easy (with zs)Intrinsic-intrinsic removal is easy (with zs) Shear-intrinsic is harder. However:Shear-intrinsic is harder. However:

massive galaxies largely responsiblemassive galaxies largely responsible If present, it gives a B-mode signatureIf present, it gives a B-mode signature Redshift-dependence is as expected:Redshift-dependence is as expected:

Contamination signal proportional to DL DLS/DS Heymans, AFH et al 2006Aid to removalKing 2005 - template fitting

Why project at all? Why project at all?

With distance information, we have a 3D With distance information, we have a 3D SHEAR FIELD, sampled at various points.SHEAR FIELD, sampled at various points.

3D Lensing3D Lensing

+ z+ z

2½D lensing in slices2½D lensing in slices

Hu 1999Dividing the source distribution Dividing the source distribution improves parameter estimationimproves parameter estimation

3D cosmic shear3D cosmic shear

)(ðð2

1)( rr

• Shear is a spin-weight 2 fieldShear is a spin-weight 2 field

• Spin weight is Spin weight is s:s: under rotation of under rotation of coordinate axes bycoordinate axes by ψψ, , A → Aexp(iA → Aexp(issψψ))

• In general, a spin-weight 2 field can be In general, a spin-weight 2 field can be written aswritten as

==½ðð (½ðð (EE+i +i BB))

Castro, AFH, Kitching Phys Rev D Castro, AFH, Kitching Phys Rev D 20052005

Real 1 imag i2

)())((2

1)( rr yxyx ii

= 1+i2

Relationship to dark matter field:Relationship to dark matter field:Natural expansion of shear is spherical Bessel functions and spin-weight 2 spherical harmonics. For small-angle surveys (Heavens, Kitching & Taylor astroph Monday)

ggalaxiesgyxi iXkrjrk ).exp()(),(

2),,(

)';,'()''(')'1('

11'

)()()|(),(

)(

0

0

20

tkrkjdkzrr

dr

krjznzzpdzdzHk

zr

ppm

Transform of the shear field

Integral nature of lensing

Include photo-z errors

Transform of density fieldz and r

CMB: PlanckCMB: Planck

BAO: WFMOS 2000 sq deg to z=1BAO: WFMOS 2000 sq deg to z=1

SNe: 2000 to z=1.5SNe: 2000 to z=1.5

Combination with other experimentsCombination with other experiments

Planck + 3D WL

Combining 3D lensing, CMB, BAO, Combining 3D lensing, CMB, BAO, SNeSNe

DARK ENERGY: Assume w(a)=w0+wa(1-a)

3.5% accuracy on w at z=0 ~1% on w(z) at z~0.4

Geometric Dark Energy TestGeometric Dark Energy Test

Depends only on global geometry of Universe: Depends only on global geometry of Universe: ΩΩVV, , ΩΩmm and and w.w. Independent of structure.Independent of structure.

(Jain & Taylor, 2003, Taylor, Kitching, Bacon, AFH astroph last week)

ObserverObserver Galaxy cluster/lensGalaxy cluster/lensz2

z1zL

)]()()[(

)]()()[(R ,

),(

),(),,(

dependence geometricpurely a has shears of ratio The

21

12

2

1

L

L

L

LmV zrzrzr

zrzrzr

zz

zzwR

SystematicsSystematics Can marginalise over ‘nuisance’ parameters, such as a Can marginalise over ‘nuisance’ parameters, such as a

bias in the photo-zsbias in the photo-zs Quick check on such errors from expected shift of Quick check on such errors from expected shift of

maximum likelihood point:maximum likelihood point:

Shift in estimate of w Shift in estimate of w ~ 1.2~ 1.2 x mean error in photo-zs x mean error in photo-zs (Shear ratio is more affected: (Shear ratio is more affected: 9 x9 x))

3D shear power seems less sensitive to this error than 3D shear power seems less sensitive to this error than tomography tomography (Huterer et al 2005, Ma et al 2005)(Huterer et al 2005, Ma et al 2005)

May require fewer calibrating spectroscopic redshiftsMay require fewer calibrating spectroscopic redshifts

Kim et al 2004; Taylor et al 2006; Heavens et al 2006

F=Generalised Fisher matrix

ConclusionsConclusions Dark Energy and Dark Matter are now Dark Energy and Dark Matter are now

key scientific goals of cosmologykey scientific goals of cosmology

Lensing in 3D is very powerful: Lensing in 3D is very powerful: accuracies of accuracies of ~1-3% on w~1-3% on w potentially potentially possiblepossible

Physical systematics can be controlledPhysical systematics can be controlled

Large-scale photometric redshift survey Large-scale photometric redshift survey with extremely good image quality is with extremely good image quality is needed ~10000 sq deg, median z~0.7needed ~10000 sq deg, median z~0.7

Space (imaging) + ground (photozs)Space (imaging) + ground (photozs)