Does Bose-Einstein condensation of CMB photons cancel {\mu} distortions
  created by dissipation of sound waves in the early Universe?
  The difference in the adiabatic indices of photons and non-relativistic
baryonic matter in the early Universe causes the electron temperature to be
slightly lower than the radiation temperature. Thermalization of photons with a
colder plasma results in the accumulation of photons in the Rayleigh-Jeans
tail, aided by stimulated recoil, while the higher frequency spectrum tries to
approach Planck spectrum at the electron temperature
$T_{\gamma}^{final}=\Te<T_{\gamma}^{initial}$; i.e., Bose-Einstein condensation
of photons occurs. We find new solutions of the Kompaneets equation describing
this effect. No actual condensate is, in reality, possible since the process is
very slow and photons drifting to low frequencies are efficiently absorbed by
bremsstrahlung and double Compton processes. The spectral distortions created
by Bose-Einstein condensation of photons are within an order of magnitude (for
the present range of allowed cosmological parameters), with exactly the same
spectrum but opposite in sign, of those created by diffusion damping of the
acoustic waves on small scales corresponding to comoving wavenumbers $45< k<
10^4\, Mpc^{-1}$. The initial perturbations on these scales are completely
unobservable today due to their being erased completely by Silk damping. There
is partial cancellation of these two distortions, leading to suppression of
$\mu$ distortions expected in the standard model of cosmology. The net
distortion depends on the scalar power index $n_S$ and its running $d n_S/d\ln
k$, and may vanish for special values of parameters, for example, for a running
spectrum with, $n_S=1,d n_S/d\ln k=-0.038$. We arrive at an intriguing
conclusion: even a null result, non-detection of $\mu$-type distortion at a
sensitivity of $10^{-9}$, gives a quantitative measure of the primordial
small-scale power spectrum.
