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. 
Rishi Khatri and Rashid A. Sunyaev
astro-ph.CO hep-ph hep-th