When Freeze-out occurs due to a non-Boltzmann suppression: A study of
  degenerate dark sector
  Exponential suppression or commonly known as the Boltzmann suppression in the
number density of dark matter is the key ingredient for creating chemical
imbalance prior to the usual thermal freeze-out. A degenerate/quasi-degenerate
dark sector can experience a different exponential suppression in the number
density analogous to the radioactive decay law leading to a delayed freeze-out
mechanism of dark matter known as the co-decaying dark matter. In this work, we
study the dynamics of a multicomponent dark matter from thermally decoupled
degenerate dark sector in a hidden U$(1)_{X}$ extension of the Standard Model.
We compute the relic density of dark matter frozen-out through the co-decaying
mechanism by solving four coupled Boltzmann equations. We demonstrate how
temperature $T^\prime $ of the dark sector changes due to all types of
$3\rightarrow 2$ and $2\rightarrow 2$ interactions along with the eternal
expansion of the Universe. We find that $3\rightarrow 2$ interactions enhance
$T^\prime$ by producing energetic particles in the dark sector while the excess
heat is transferred by $2\rightarrow 2$ interactions to the entire dark sector.
As the direct detection is possible only through the feeble portal couplings,
we investigate the neutrino and $\gamma$-ray signals from dark matter
annihilation via one step cascade processes and compare our results with the
measured fluxes of atmospheric neutrinos by Super-Kamiokande and diffuse
$\gamma$-rays by Fermi-LAT, EGRET, INTEGRAL collaborations. We find that the
present scenario easily evades all the existing bounds from atmospheric
neutrino and diffuse $\gamma$-ray observations for degenerate dark sector.
However, the constraints are significant for quasi degenerate scenario.
