The existence of an extra species over the radiation background composed of the Standard Model particles, prior to the Big Bang Nucleosynthesisleads (BBN), leads to a fast expanding Universe driven by an enhanced Hubble parameter. This can revive the under-abundant WIMP dark matter by causing freeze-out earlier without modifying the interaction strength between dark matter and thermal bath. In this talk, I will elaborately demonstrate this effect in the context of a TeV scale pure triplet fermionic dark matter which has already been ruled out by the combination of relic density and indirect detection bounds for the radiation dominated background. Moreover, the dynamical generation of lepton asymmetry (e.g. asymmetry generation and wash-out processes) due to heavier Z2 even triplet fermions is also affected by the modification in Hubble parameter, particularly, the mass bound of the former can be relaxed by generating adequate CP asymmetry at the lower mass scale.
Towards the end of the talk, I will show a concrete example where a different cosmological evolution of the Universe, in the pre-BBN era, can be realized from the modification in the Einstein gravity.