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During cosmic recombination, charged particles bind into neutral atoms andthe mean free path of photons rapidly increases, resulting in the familiardiffusion damping of primordial radiation temperature variations. An additionaleffect is a small photon spectrum distortion, because photons arriving from aparticular sky direction were originally in thermal equilibrium at variousspatial locations with different temperatures; the combination of thesedifferent blackbody temperature distributions results in a spectrum with aCompton $y$-distortion. Using the approximation that photons had zero mean freepath prior to their second-to-last scattering, we derive an expression for theresulting $y$-distortion, and compute the angular correlation function of thediffusion $y$-distortion and its cross-correlation with the square of thephoton temperature fluctuation. Detection of the cross-correlation is withinreach of existing arcminute-resolution microwave background experiments such asthe Atacama Cosmology Telescope and the South Pole Telescope.

Angular Correlations of Cosmic Microwave Background Spectrum Distortions from Photon Diffusion