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CMB and cluster lensing

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. Weak lensing of the CMB. Last scattering surface. Inhomogeneous universe

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CMB and cluster lensing

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  1. 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

  2. Weak lensing of the CMB Last scattering surface Inhomogeneous universe - photons deflected Observer

  3. Lensing order of magnitudes Ψ β Newtonian argument: β = 2 Ψ General Relativity: β = 4 Ψ (β << 1) Potentials linear and approx Gaussian: Ψ~ 2 x 10-5 β ~ 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.)

  4. 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

  5. Full calculation: deflection angle on sky given in terms of lensing potential Lensed temperature given by Lewis 2005,astro-ph/0502469 LensPix sky simulation code:http://cosmologist.info/lenspix

  6. 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

  7. 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)

  8. Polarization lensing: Cx and CE Important ~ 10% smoothing effect

  9. 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

  10. Polarization power spectra Current 95% indirect limits for LCDM given WMAP+2dF+HST Lewis, Challinor : astro-ph/0601594; Lewis Moriond 2006

  11. 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 < T T T > - Zero unless correlation <T Ψ> • Large scale signal from ISW-induced T- Ψ correlation • Small scale signal from non-linear SZ – Ψ correlation Zaldarriaga astro-ph/9910498, Goldberg&Spergel, etc…

  12. Trispectrum: Connected four-point < T T T T>c • Depends on deflection angle and temperature power spectra • ‘Easily’ measurable for accurate ell > 1000 observations Zaldarriaga astro-ph/9910498; Hu astro-ph/0105117 Other signatures • correlated hot-spot ellipticities • Higher n-point functions • Polarization non-Gaussianity

  13. 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

  14. 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 >~ 20 Lensing probably not main problem for flat quadrilaterals if single-field non-Gaussianity No analysis of relative shape-dependence from e.g. curvaton??

  15. 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

  16. 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

  17. Add polarization observations? Difference after cluster lensing Unlensed T+Q+U Less sample variance – but signal ~10x smaller: need 10x lower noise Note: E and B equally useful on these scales; gradient could be either

  18. 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 (< 0.1μK)- Re-scattered thermal SZ (freq)- Kinetic SZ (higher order)- Other lensesGenerally much cleaner

  19. 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 γab = ∂<a αb> • Constrain cluster parameters from predicted shear • Assume numerous systematics negligible…

  20. Optimistic Futuristic CMB polarization lensing vs galaxy lensingLess massive case: M = 2 x 1014 h-1 Msun, c=5 CMB polarization only (0.07 μK arcmin noise) Galaxies (500 gal/arcmin2)

  21. Summary • Weak lensing of the CMB very important for precision cosmology- changes power spectra- potential confusion with primordial gravitational waves for r <~ 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

  22. 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 Hu’s talk

  23. Full calculation: Lensed temperature depends on deflection angle: Lensing Potential Deflection angle on sky given in terms of lensing potential

  24. Toy model: spherically symmetric NFW cluster 2 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

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