Secondary CMB Anisotropy - Wayne Hu's Tutorials
Secondary CMB Anisotropy - Wayne Hu's Tutorials
Secondary CMB Anisotropy - Wayne Hu's Tutorials
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• Taylor expand<br />
Θ(ˆn) = ˜ Θ(ˆn + ∇φ)<br />
Flat-sky Treatment<br />
= ˜ Θ(ˆn) + ∇iφ(ˆn)∇ i ˜ Θ(ˆn) + 1<br />
2 ∇iφ(ˆn)∇jφ(ˆn)∇ i ∇ j ˜ Θ(ˆn) + . . .<br />
• Fourier decomposition<br />
φ(ˆn) =<br />
˜Θ(ˆn) =<br />
<br />
<br />
d2l φ(l)eil·ˆn<br />
(2π) 2<br />
d 2 l<br />
(2π) 2 ˜ Θ(l)e il·ˆn
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