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The difference in the adiabatic indices of photons and non-relativisticbaryonic matter in the early Universe causes the electron temperature to beslightly lower than the radiation temperature. Thermalization of photons with acolder plasma results in the accumulation of photons in the Rayleigh-Jeanstail, aided by stimulated recoil, while the higher frequency spectrum tries toapproach Planck spectrum at the electron temperature$T_{\gamma}^{final}=\Te<T_{\gamma}^{initial}$; i.e., Bose-Einstein condensationof photons occurs. We find new solutions of the Kompaneets equation describingthis effect. No actual condensate is, in reality, possible since the process isvery slow and photons drifting to low frequencies are efficiently absorbed bybremsstrahlung and double Compton processes. The spectral distortions createdby Bose-Einstein condensation of photons are within an order of magnitude (forthe present range of allowed cosmological parameters), with exactly the samespectrum but opposite in sign, of those created by diffusion damping of theacoustic waves on small scales corresponding to comoving wavenumbers $45< k<10^4\, Mpc^{-1}$. The initial perturbations on these scales are completelyunobservable today due to their being erased completely by Silk damping. Thereis partial cancellation of these two distortions, leading to suppression of$\mu$ distortions expected in the standard model of cosmology. The netdistortion depends on the scalar power index $n_S$ and its running $d n_S/d\lnk$, and may vanish for special values of parameters, for example, for a runningspectrum with, $n_S=1,d n_S/d\ln k=-0.038$. We arrive at an intriguingconclusion: even a null result, non-detection of $\mu$-type distortion at asensitivity of $10^{-9}$, gives a quantitative measure of the primordialsmall-scale power spectrum.

Does Bose-Einstein condensation of CMB photons cancel {\mu} distortions created by dissipation of sound waves in the early Universe?