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The Boltzmann equation describes the evolution in time
of the
spatial (
) and angular (
) distribution of the radiation
under gravity and scattering processes. In the notation of [1], it
can be written implicitly as
| ![\begin{displaymath}
{d \over d\eta} \vec{T}(\eta,\vec{x},\hat{n}) \equiv
{\part...
...vec{T}_{\vert i}
= \vec{C}[\vec{T}] + \vec{G}[h_{\mu\nu}] \, ,\end{displaymath}](img52.gif) |
(14) |
where
encapsulates the perturbation
to the temperature
and the polarization
(Stokes Q and U parameters) in units of the temperature fluctuation.
The term
accounts for collisions, here Compton scattering of the
photons with the electrons,
while the term
accounts for gravitational redshifts.
Wayne Hu
9/9/1997