CMB%20and%20cluster%20lensing

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CMB and cluster lensing

• Antony Lewis
• Institute of Astronomy, Cambridge
• http//cosmologist.info/

Lewis Challinor, Phys. Rept. 2006
astro-ph/0601594
Lewis King, PRD 2006 astro-ph/0512104
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Weak lensing of the CMB
Last scattering surface
Inhomogeneous universe - photons deflected
Observer
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Lensing order of magnitudes
?
ß
Newtonian argument ß 2 ? General
Relativity ß 4 ?
(ß ltlt 1)
Potentials linear and approx Gaussian ? 2 x
10-5
ß 10-4
Characteristic size from peak of matter power
spectrum 300Mpc
Comoving distance to last scattering surface
14000 MPc
total deflection 501/2 x 10-4
pass through 50 lumps
2 arcminutes
assume uncorrelated
(neglects angular factors, correlation, etc.)
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So why does it matter?

• 2arcmin ell 3000- on small scales CMB is
  very smooth so lensing dominates the linear
  signal
• Deflection angles coherent over 300/(14000/2)
  2 - comparable to CMB scales- expect
  2arcmin/60arcmin 3 effect on main CMB acoustic
  peaks

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Full calculation deflection angle on sky given
in terms of lensing potential
Lensed temperature given by
LensPix sky simulation codehttp//cosmologist.in
fo/lenspix
Lewis 2005,astro-ph/0502469
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Lensed temperature Cl
and
linear in lensing potential power spectrum
Analogous results for CMB polarization.
Essentially exact to order of weak lensing
very well understood effect on power
spectra.Non-linear Pk 0.2 on TT, 5 on BB
Lewis, Challinor Phys. Rept. 2006
astro-ph/0601594
Full-sky fully non-perturbative generalization of
method by Seljak 1996
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Lensing effect on CMB temperature power
spectrum smoothing of acoustic peaks small
scale power
Full-sky calculation accurate to 0.1 Fortran
code CAMB (http//camb.info)
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Polarization lensing Cx and CE
Important 10 smoothing effect
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Polarization lensing CB
Nearly white BB spectrum on large scales
Lensing effect can be largely subtracted if only
scalar modes lensing present, but approximate
and complicated (especially posterior
statistics).Hirata, Seljak astro-ph/0306354,
Okamoto, Hu astro-ph/0301031
Lewis, Challinor astro-ph/0601594
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Polarization power spectra
Current 95 indirect limits for LCDM given
WMAP2dFHST
Lewis, Challinor astro-ph/0601594 Lewis
Moriond 2006
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Non-Gaussianity

• Unlensed CMB expected to be close to Gaussian
• With lensing

• For a FIXED lensing field, lensed field also
  Gaussian
• For VARYING lensing field, lensed field is
  non-Gaussian

Three point function Bispectrum lt T T T gt
- Zero unless correlation ltT ?gt

• Large scale signal from ISW-induced T- ?
  correlation
• Small scale signal from non-linear SZ ?
  correlation

Zaldarriaga astro-ph/9910498, GoldbergSpergel,
etc
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• Trispectrum Connected four-point lt T T T Tgtc

• Depends on deflection angle and temperature
  power spectra
• Easily measurable for accurate ell gt 1000
  observations

Zaldarriaga astro-ph/9910498 Hu astro-ph/0105117
Other signatures

• correlated hot-spot ellipticities
• Higher n-point functions
• Polarization non-Gaussianity

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Confusion with primordial non-Gaussianity?

• 1-point function

• lensing only moves points around, so
  distribution at a point Gaussian
• But complicated by beam effects

Kesden, Cooray, Kamionkowski astro-ph/0208325

• Bispectrum

- ISW-lensing correlation only significant on
very large scales
- SZ-lensing correlation can dominate on very
small scales
- On larger scales oscillatory primordial signal
should be easily distinguishable with Planck if
large enough
Komatsu astro-ph/0005036
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• Trispectrum (4-point)

Basic inflation- most signalin long thin
quadrilaterals
Lensing- broader distribution, lesssignal in
thin shapes
Komatsu astro-ph/0602099
Hu astro-ph/0105117
Can only detect inflation signal from cosmic
variance if fNL gt 20
Lensing probably not main problem for flat
quadrilaterals if single-field non-Gaussianity
No analysis of relative shape-dependence from
e.g. curvaton??
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Cluster CMB lensinge.g. to constrain cosmology
via number counts
Lewis King, astro-ph/0512104
Following Seljak, Zaldarriaga, Dodelson, Vale,
Holder, etc.
CMB very smooth on small scales approximately a
gradient
What we see
Last scattering surface
GALAXYCLUSTER
0.1 degrees
Need sensitive arcminute resolution observations
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RMS gradient 13 µK / arcmindeflection from
cluster 1 arcmin
Lensing signal 10 µK
BUT depends on CMB gradient behind a given
cluster
Unlensed
Lensed
Difference
Unlensed CMB unknown, but statistics well
understood (background CMB Gaussian)
can compute likelihood of given lens (e.g. NFW
parameters) essentially exactly
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Add polarization observations?
Difference after cluster lensing
Unlensed TQU
Less sample variance but signal 10x smaller
need 10x lower noise
Note E and B equally useful on these scales
gradient could be either
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Complications

• Temperature - Thermal SZ, dust, etc. (frequency
  subtractable) - Kinetic SZ (big problem?) -
  Moving lens effect (velocity Rees-Sciama,
  dipole-like) - Background Doppler signals -
  Other lenses

• Polarization - Quadrupole scattering (lt
  0.1µK)- Re-scattered thermal SZ (freq)- Kinetic
  SZ (higher order)- Other lensesGenerally much
  cleaner

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Is CMB lensing better than galaxy lensing?

• Assume background galaxy shapes random before
  lensing
• Measure ellipticity after lensing by cluster

Lensing

• On average ellipticity measures reduced shear
• Shear is ?ab ?lta abgt
• Constrain cluster parameters from predicted shear
• Assume numerous systematics negligible

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Optimistic Futuristic CMB polarization lensing vs
galaxy lensingLess massive case M 2 x 1014
h-1 Msun, c5
CMB polarization only (0.07 µK arcmin noise)
Galaxies (500 gal/arcmin2)
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Summary

• Weak lensing of the CMB very important for
  precision cosmology- changes power spectra-
  potential confusion with primordial gravitational
  waves for r lt 10-3- Non-Gaussian signal, but
  well known and probably not main problem
• Cluster lensing of CMB- Temperature lensing
  difficult because of confusions- CMB
  polarisation lensing needs high sensitivity but
  potentially useful at high redshift- galaxy
  lensing expected to be much better for low
  redshift clusters- CMB lensing has quite
  different systematics to galaxy lensing

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Planck (2007) parameter constraint simulation
(neglect non-Gaussianity of lensed field)
Lewis 2005,astro-ph/0502469
Important effect, but using lensed CMB power
spectrum gets right answer
Parameters can be improved using BB/lensing
reconstruction non-Gaussianity important in the
future c.f. Wayne Hus talk
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Full calculation Lensed temperature depends on
deflection angle
Lensing Potential
Deflection angle on sky given in terms of lensing
potential
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Toy model spherically symmetric NFW cluster
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M200 1015 h-1 Msun
Deflection 0.7 arcmin
c 5, z 1 (rv 1.6Mpc)
(approximate lens as thin, constrain projected
density profile)
assume we know where centre is