Lensed CMB power spectra from all-sky correlation functions(13)

Weak lensing of the CMB changes the unlensed temperature anisotropy and polarization power spectra. Accounting for the lensing effect will be crucial to obtain accurate parameter constraints from sensitive CMB observations. Methods for computing the lensed

negligibly(seeAppendixCforthefullresult).We ndthefollowingresultsforthelensedpolarizationcorrelationfunctionstosecondorderinCgl,2:

+≈ξ

2l+1

lmm′

(ClE ClB)

X0222dl2 2+Cgl,2[X1212dl1 1+X1322dl

4π

3 3]

+

1

C2XlX

022X000dl02+Cgl,2

000

′

4π

Xl(l+(X112dl11+X132dl

1)

3 1)

+1

2

2

4

4π

(ClE+ClB)=

2l+1

l

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