Beyond y and \mu: the shape of the CMB spectral distortions in the
  intermediate epoch, 1.5x10^4 < z < 2x10^5
  We calculate numerical solutions and analytic approximations for the
intermediate-type spectral distortions. Detection of a \mu-type distortion
(saturated comptonization) in the CMB will constrain the time of energy
injection to be at a redshift 2x10^6> z > 2x10^5, while a detection of a y-type
distortion (minimal comptonization) will mean that there was heating of CMB at
redshift z< 1.5x10^4. We point out that the partially comptonized spectral
distortions, generated in the redshift range 1.5x10^4 < z x 2x10^5, are much
richer in information than the pure y and \mu-type distortions. The spectrum
created during this period is intermediate between y and \mu-type distortions
and depends sensitively on the redshift of energy injection. These
intermediate-type distortions cannot be mimicked by a mixture of y and \mu-type
distortions at all frequencies and vice versa. The measurement of these
intermediate-type CMB spectral distortions has the possibility to constrain
precisely not only the amount of energy release in the early Universe but also
the mechanism, for example, particle annihilation and Silk damping can be
distinguished from particle decay. The intermediate-type distortion templates
and software code using these templates to calculate the CMB spectral
distortions for user-defined energy injection rate are made publicly available.
