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Constraining The Distance-Redshift Relation Through Strong Gravitational Lensing of the CMB. Paul Stankus Oak Ridge National Lab APS April 19,2005. You all know…. Distance. Measuring z ( t ), or z (distance), reveals expansion history of the Universe. Redshift.

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Constraining the distance redshift relation through strong gravitational lensing of the cmb

Constraining The Distance-Redshift Relation Through Strong Gravitational Lensing of the CMB

Paul Stankus

Oak Ridge National Lab

APS April 19,2005


You all know
You all know… Gravitational Lensing of the CMB

Distance

Measuring z(t), or z(distance), reveals expansion history of the Universe

Redshift


Gravitational bending of light
Gravitational Bending of Light Gravitational Lensing of the CMB

S’

Source

a

b

J

b

M

Observer

Lens

Angular Distances (non-Euclidean)

DOL

DLS

DOS


Strong lensing and the einstein ring
Strong Lensing and the Einstein Ring Gravitational Lensing of the CMB

S’

S

M

L

O

JEinstein


Cosmological angular distances
Cosmological Angular Distances Gravitational Lensing of the CMB

t

Basic measure c(z1,z2) = comoving distance between event of photon emitted at z2 and observed at z1

(Bartelmann & Schneider, Phys Rep 340 (2001) 291-472)

c(0,zS)

c(0,zL)

c(zL,zS)

O

Slope 1

x

Slope 1/(1+zL)

L

S

Angular diameter distance Dang(z1,z2)=c(z1,z2)/(1+ z2)

Slope 1/(1+zS)


Coincident double strong lensing

M Gravitational Lensing of the CMB

L

O

SN

Coincident Double Strong Lensing

SF

If we measure QEN2/QEF2 and know cOL(zL) andcOSN(zSN)

then we can map cOSF(zSF) and measure distance as a function of redshift without knowledge of lens mass.


The cmb shines behind everything
The CMB Shines Behind Everything Gravitational Lensing of the CMB

CMB

M

L

O

Distant Galaxy

Plan 1: Know cOL(zL), cODG(zDG) via Hubble; learn cOCMB

Plan 2: Know cOL(zL), assume cOCMB fixed; mapcODG(zDG)


Einstein Rings in the CMB Image Gravitational Lensing of the CMB

Expect axi-symmetric strong lens to produce one band (thick isotherm) in the image plane with a unique “F” topology

Inner and outer critical curves

Outer and inner caustics

Source Plane

Image Plane


Some work by actual experts
Some work by Gravitational Lensing of the CMBactual experts

Simulated CMB temperature field (left) and image after lensing by a galaxy cluster (right) Bartelmann astro-ph/0304162. The “F” feature is clearly visible in the lensed image.


Rude reality
Rude Reality Gravitational Lensing of the CMB

In extended lenses mass may lie outside Einstein rings

Real lenses are not axi-symmetric; inner caustic no longer degenerate at a point, no “true” Einstein ring

The real CMB is not a pure gradient

Need high spatial resolution (sub-arc-minute) measurement of CMB anisotropies (1 in 105-6 precision)

My conjecture: Even in the real world, strong lensing of the CMB will produce a singular thick isotherm with a unique “F” topology, and the loop area will still correspond to 4pMDLCMB/DOLDOCMB


Partial reading list
(Partial) Reading List Gravitational Lensing of the CMB

Seljak & Zaldarriaga “Lensing Induced Cluster Signatures in Cosmic Microwave Background” astro-ph/9907254

Dodelson & Starkman, “Galaxy-CMB Lensing”, astro-ph/0305467; Dodelson, “CMB-Cluster Lensing”, astro-ph/0402314

Maturi et al., “Gravitational lensing of the CMB by galaxy clusters”, astro-ph/0408064

Holder & Kosowsky, “Gravitational Lensing of the Microwave Background by Galaxy Clusters”, astro-ph/0401519

The subject of GLCMB is taking off! Most work to date has been on using GLCMB to reconstruct mass distributions in clusters. The utility of coincident double strong lensing is relatively under-explored at present.


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