= Angular-scale limits of instantaneous photon decoupling
Approximating decoupling by a single time and retaining only a photon monopole and Doppler dipole omits the finite <cosmological visibility function> width, diffusion or <Silk damping>, quadrupole anisotropy and polarization generated as <tight coupling> fails. The <photon-baryon acoustic oscillator> also make the emission density and velocity strongly scale dependent. They can be included in the initial monopole and dipole, so their existence alone does not invalidate the subsequent collisionless <line-of-sight solution for free-streaming photons>. Smaller angles correspond to larger angular multipole $\ell$.
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