= Collisionless preservation of a Planck spectrum
Let the scale factor grow by $f$ from an initially thermal <photon> distribution. <geodesic> redshift gives $\nu_i=f\nu$, and conserving <photons> in corresponding comoving <frequency> bins gives $n_\nu(t)=f^{-2}n_{f\nu}(t_i)$. Inserting <Planck's law> leaves the same spectral form at <temperature> $T_i/f$. Total photon-number conservation alone would not prove that the entire <radiation spectrum> stays Planckian; <frequency> redshift and collisionless propagation are also required. Absorption, injection or spectral mixing can invalidate this one-temperature argument.
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