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### Description

The indirect searches of Dark Matter (DM), in conjugation with the

so called `missing track searches' at the collider seems to confine fermion

triplet DM mass within a narrow range around $1$ TeV. The canonical picture of

pure triplet fermionic dark matter is in tension since it is under-abundant for

the said mass range. Several preceding studies have shown that the existence of

an extra species over the radiation background composed of the Standard Model particles,

prior to the Big Bang Nucleosynthesis, leads to a fast expanding Universe driven by

an enhanced Hubble parameter. This faster (than radiation) expansion has the potential

to revive the under-abundant fermion triplet ($\mathbb{Z}_2$ odd, lightest generation)

WIMP dark matter scenario by causing freeze-out earlier without modifying the interaction

strength between dark matter and thermal bath. Although the CP asymmetry, produced due to the

decay of $\mathbb{Z}_2$ even heavier generations of the triplet, remains unaffected by

the modification of cosmology, the evolution of the same receives significant non-trivial

effect. It has been observed through numerical estimations that the minimum mass

of the decaying triplet, required to produce sufficient baryon asymmetry, can be lowered

up to two orders (compared to the standard cosmology) in this fast expansion scenario. The

non-standard parameters $n$ and $T_r$, which simultaneously control the dark matter relic abundance

as well the frozen value of baryon asymmetry, are tightly constrained due to consecutive

imposition of experimental bounds on relic density followed by observed value of baryon

asymmetry of the Universe. It has been found that $n$ is strictly bounded within the

interval $0.4\lesssim n \lesssim 1.8$. The upper bound is imposed by the

baryon asymmetry constraint whereas the lower bound arises to satisfy the

correct relic abundance of the DM. The restriction on the other non-standard

parameter $T_r$ is not so stringent as it can vary from sub GeV to few tens of GeV.