Download presentation

Presentation is loading. Please wait.

Published byJada Wallace Modified over 4 years ago

1
Weak Lensing of the CMB Antony Lewis Institute of Astronomy, Cambridge http://cosmologist.info/

2
From the beginning Lensing order of magnitudes Lensed power spectrum Effect on CMB polarization Cluster masses from CMB lensing Outline

3
Hu & White, Sci. Am., 290 44 (2004) Evolution of the universe Opaque Transparent

4
Source: NASA/WMAP Science Team O(10 -5 ) perturbations (+galaxy) Dipole (local motion) (almost) uniform 2.726K blackbody Observations: the microwave sky today

5
Where do perturbations come from? Quantum Mechanics waves in a box calculation vacuum state, etc… Inflation make >10 30 times bigger After inflation Huge size, amplitude ~ 10 -5 New physicsKnown physics

6
Perturbation evolution – what we actually observe CMB monopole source till 380 000 yrs (last scattering), linear in conformal time scale invariant primordial adiabatic scalar spectrum photon/baryon plasma + dark matter, neutrinos Characteristic scales: sound wave travel distance; diffusion damping length

7
Hu & White, Sci. Am., 290 44 (2004) CMB temperature power spectrum Primordial perturbations + later physics diffusion damping acoustic oscillations primordial power spectrum finite thickness

8
Weak lensing of the CMB Last scattering surface Inhomogeneous universe - photons deflected Observer

9
Lensing order of magnitudes β Newtonian argument: β = 2 Ψ General Relativity: β = 4 Ψ Ψ 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 pass through ~50 lumps assume uncorrelated total deflection ~ 50 1/2 x 10 -4 ~ 2 arcminutes (neglects angular factors, correlation, etc.) (β << 1)

10
So why does it matter? 2arcmin: ell ~ 3000 - o n 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

11
Full calculation: Lensed temperature depends on deflection angle: Lensing Potential Deflection angle on sky given in terms of lensing potential

12
Deflections O(10 -3 ), but coherent on degree scales important! Deflection angle power spectrum Computed with CAMB: http://camb.info

13
LensPix sky simulation code: http://cosmologist.info/lenspix Lewis 2005 http://cosmologist.info/lenspix

14
Lensing effect on CMB temperature power spectrum Full-sky calculation accurate to 0.1%: Challinor & Lewis 2005, astro-ph/0502425

15
Planck (2007+) parameter constraint simulation (neglect non-Gaussianity of lensed field) Important effect, but using lensed CMB power spectrum gets right answer Lewis 2005, astro-ph/0502469

16
Thomson Scattering Polarization W Hu

17
CMB Polarization Generated during last scattering (and reionization) by Thomson scattering of anisotropic photon distribution Hu astro-ph/9706147

18
Polarization: Stokes Parameters - - QU Q -Q, U -U under 90 degree rotation Q U, U -Q under 45 degree rotation Rank 2 trace free symmetric tensor

19
E and B polarization gradient modes E polarization curl modes B polarization e.g. B modes only expected from gravitational waves and CMB lensing e.g. cold spot

20
Why polarization? E polarization from scalar, vector and tensor modes (constrain parameters, break degeneracies) B polarization only from vector and tensor modes (curl grad = 0) + non-linear scalars

21
Polarization lensing: C B 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

22
Polarization lensing: C x and C E Lewis, Challinor : astro-ph/0601594

23
Primordial Gravitational Waves Well motivated by some inflationary models - Amplitude measures inflaton potential at horizon crossing - distinguish models of inflation Observation would rule out other models - ekpyrotic scenario predicts exponentially small amplitude - small also in many models of inflation, esp. two field e.g. curvaton Weakly constrained from CMB temperature anisotropy - significant power only at l<100, cosmic variance limited to 10% - degenerate with other parameters (tilt, reionization, etc) Look at CMB polarization: B-mode smoking gun

24
Current 95% indirect limits for LCDM given WMAP+2dF+HST Polarization power spectra Lewis, Challinor : astro-ph/0601594

25
Cluster CMB lensing GALAXY CLUSTER Last scattering surface What we see Following: Seljak, Zaldarriaga, Dodelson, Vale, Holder, etc. CMB very smooth on small scales: approximately a gradient Lewis & King, astro-ph/0512104 0.1 degrees

26
Toy model: spherically symmetric NFW cluster M 200 ~ 10 15 h -1 M sun c ~ 5, z ~ 1 (r v ~ 1.6Mpc) Deflection ~ 0.7 arcmin (approximate lens as thin, constrain projected density profile) assume we know where centre is 2

27
UnlensedLensedDifference RMS gradient ~ 13 μK / arcmin deflection from cluster ~ 1 arcmin Lensing signal ~ 10 μK BUT: depends on CMB gradient behind a given cluster

28
Constraining cluster parameters Calculate P(c,M 200 | observation) Simulated realisations with noise 0.5 μK arcmin, 0.5 arcmin pixels Somewhat futuristic: 160x lower noise 14x higher resolution than Planck; few times better than ACT CMB approximately Gaussian – know likelihood function

29
Unlensed T+Q+U Difference after cluster lensing Add polarization observations? Less sample variance – but signal ~10x smaller: need 10x lower noise Plus side: SZ (etc) fractional confusion limit probably about the same as temperature

30
0.5 μK arcmin 0.7 μK arcmin0.07 μK arcmin TemperaturePolarisation Q and U Noise: less dispersion in error

31
Is it better than galaxy lensing? Assume galaxy shapes random before lensing Measure ellipticity after lensing Lensing On average ellipticity measures reduced shear Shear is γ ab = Constrain cluster parameters from predicted shear

32
Galaxy lensing comparison Massive case: M = 10 15 h -1 M sun, c=5 CMB temperature only (0.5 μK arcmin noise)Galaxies (100 gal/arcmin 2 ) (from expected log likelihoods) Ground (30/arcmin)

33
CMB temperature only (0.07 μK arcmin noise) Optimistic Futuristic CMB polarization vs galaxy lensing Less massive case: M = 2 x 10 14 h -1 M sun, c=5 Galaxies (500 gal/arcmin 2 )

34
CMB 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) - Kinetic SZ (higher order) - Other lenses Generally much cleaner

35
Rest frame of CMB: Redshifted colder Blueshifted hotter Moving Lenses and Dipole lensing Homogeneous CMB Rest frame of lens:Dipole gradient in CMB Deflected from colderdeflected from hotter v T = T 0 (1+v cos θ) `Rees-Sciama (non-linear ISW) dipole lensing

36
Moving lenses and dipole lensing are equivalent: Dipole pattern over cluster aligned with transverse cluster velocity – source of confusion for anisotropy lensing signal NOT equivalent to lensing of the dipole observed by us, - only dipole seen by cluster is lensed (EXCEPT for primordial dipole which is physically distinct from frame-dependent kinematic dipole) Note: Small local effect on CMB from motion of local structure w.r.t. CMB (Vale 2005, Cooray 2005) Line of sight velocity gives (v/c) correction to deflection angles from change of frame: generally totally negligible

37
Observable Dipoles Change of velocity: - Doppler change to total CMB dipole - aberration of observed angles (c.f. dipole convergence) Can observe: actual CMB dipole: (non-linear) local motion + primordial contribution Can observe: Dipole aberration (dipole convergence + kinetic aberration) So: Lensing potential dipole easily observable to O(10 -5 ) - Can find zero-aberration frame to O(10 -5 ) by using zero total CMB-dipole frame - change of frame corresponds to adding some local kinematic angular aberration to convergence dipole - zero kinematic aberration and zero kinematic CMB dipole frame = Newtonian gauge

38
Convergence dipole expected ~ 5 x 10 -4

39
Summary Weak lensing of the CMB very important for precision cosmology - changes power spectra - potential confusion with primordial gravitational waves Cluster lensing of CMB - gravitational lensing so direct probe of mass (not just baryons) - mass constraints independent of galaxy lensing constraints; source redshift known very accurately, should win for high redshifts - galaxy lensing expected to be much better for low redshift clusters - polarisation lensing needs high sensitivity but cleaner and less sample variance than temperature

40
Physics Reports review: astro-ph/0601594

41
http://CosmoCoffee.info arXiv paper filtering, discussion and comments Currently 420 registered readers

42
Calculate C l by series expansion in deflection angle? Series expansion only good on large and very small scales Accurate calculation uses correlation functions: Seljak 96; Challinor, Lewis 2005 No

43
arXivJournal.org

44
Is this right? Lieu, Mittaz, ApJ L paper: astro-ph/0409048 - Claims shift in CMB peaks inconsistent with observation - ignores effect of matter. c.f. Kibble, Lieu: astro-ph/0412275 Lieu, Mittaz, ApJ paper:astro-ph/0412276 Claims large dispersion in magnifications, hence peaks washed out - Many lines of sight do get significant magnification - BUT CMB is very smooth, small scale magnification unobservable - BUT deflection angles very small - What matter is magnifications on CMB acoustic scales i.e. deflections from large scale coherent perturbations. This is small. - i.e. also wrong Large scale potentials < 10 -3 : expect rigorous linear argument to be very accurate (esp. with non-linear corrections)

Similar presentations

OK

Observational constraints and cosmological parameters Antony Lewis Institute of Astronomy, Cambridge

Observational constraints and cosmological parameters Antony Lewis Institute of Astronomy, Cambridge

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on object oriented programming with c++ book Ppt on self awareness in nursing Ppt on agriculture in india 2013 Ppt on main festivals of india Ppt on will world end in 2012 Ppt on disaster management for download Ppt on frame relay and atm Chemistry ppt on matter Ppt on heritage of indian culture Ppt on non biodegradable waste wikipedia