Rich structure of non-thermal relativistic CMB spectral distortions from
  high energy particle cascades at redshifts $z\lesssim 2\times 10^5$
  It is generally assumed that for energy injection before recombination, all
of the injected energy is dissipated as heat in the baryon-photon plasma,
giving rise to the $y$-type, $i$-type, and $\mu$-type distortions in the CMB
spectrum. We show that this assumption is incorrect when the energy is injected
in the form of energetic (i.e. energy much greater than the background CMB
temperature) particles. We evolve the electromagnetic cascades, from the
injection of high energy particles, in the expanding Universe and follow the
non-thermal component of CMB spectral distortions resulting from the
interaction of the electromagnetic shower with the background photons,
electrons, and ions. The electromagnetic shower loses a substantial fraction of
its energy to the CMB spectral distortions before the energy of the particles
in the shower has degraded to low enough energies that they can thermalize with
the background plasma. This spectral distortion is the result of the
interaction of non-thermal energetic electrons in the shower with the CMB and
thus has a shape that is substantially different from the $y$-type or $i$-type
distortions. The shape of the final \emph{non-thermal relativistic}
($ntr$-type) CMB spectral distortion depends upon the initial energy spectrum
of the injected electrons, positrons, and photons and thus has information
about the energy injection mechanism e.g. the decay or annihilation channel of
the decaying or annihilating dark matter particles. The shape of the spectral
distortion is also sensitive to the redshift of energy injection. Our
calculations open up a new window into the energy injection at $z\lesssim
2\times 10^5$ which is not degenerate with, and can be distinguished from the
low redshift thermal $y$-type distortions.
