  We study the consequence of a non-standard cosmological epoch in the early
universe on the generation of baryon asymmetry through leptogenesis as well as
dark matter abundance. We consider two different non-standard epochs: one where
a scalar field behaving like pressure-less matter dominates the early universe,
known as early matter domination (EMD) scenario while in the second scenario,
the energy density of the universe is dominated by a component whose energy
density red-shifts faster than radiation, known as fast expanding universe
(FEU) scenario. While a radiation dominated universe is reproduced by the big
bang nucleosynthesis (BBN) epoch in both the scenario, the high scale phenomena
like generation of baryon asymmetry and dark matter relic get significantly
affected. Adopting a minimal particle physics framework known as the scotogenic
model which generates light neutrino masses at one-loop level, we find that in
one specific realisation of EMD scenario, the scale of leptogenesis can be
lower than that in a standard cosmological scenario. The other non-standard
cosmological scenarios, on the other hand, can be constrained from the
requirement of successful low scale leptogenesis and generating correct dark
matter abundance simultaneously. Such a low scale scenario not only gives a
unified picture of baryon asymmetry, dark matter and origin of neutrino mass
but also opens up interesting possibilities for experimental detection.
