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In this section, we derive the complete set of evolution
for the temperature and polarization distribution
in the scalar, vector, tensor decomposition of metric fluctuations.
Though the scalar and tensor fluid results can be found elsewhere
in the literature in a different form
(see e.g. [11,10]), the total
angular momentum representation substantially simplifies the
form and aids in the interpretation of the results. The
vector derivation is new to this work.