Photon-baryon diffusion damping equation

When gravity and expansion can be neglected and

R

is constant, the photon monopole satisfies

\ddot{Θ}_{0} + \frac{k ^{2}}{3 ( 1 + R ) Γ} (\frac{R ^{2}}{1 + R} + \frac{16}{15}) \dot{Θ}_{0} + \frac{k ^{2}}{3 ( 1 + R )} Θ_{0} = 0.

The first damping contribution comes from photon-baryon velocity slip; the second comes from the photon quadrupole. This is a local form of Silk damping.

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Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 53 / 2 / iv / Solution
Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 312 / 3 / iii / Solution

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