  The expansion rate of the Universe deviates from its standard value when the
total energy density includes contribution from a new scalar field apart from
the radiation energy density. The non-trivial modifications incurred in the
Boltzmann equations render the well known analytical solutions unsuitable in
non standard scenario. In the present study we derive analytical expressions
for the efficiency factor (which is nothing but solution of set of Boltzmann
equations) using certain legible approximations. A fair degree of accuracy of
these formulas have been observed by juxtaposing the analytical results with
that obtained through numerical solution of Boltzmann equations. Faster
expansion of the Universe results in decrement of the effective decay parameter
which brings down the amount of washout of asymmetry due to inverse decay. Thus
in non-standard cosmology scenario, a larger fraction of the asymmetry
(generated at early epoch) is expected to survive till present epoch.
Alteration of the cosmology does not affect the underlying particle physics
model responsible for the generation of the CP asymmetry. Therefore starting
from an identical particle physics model we will end up with a larger final
baryon asymmetry in the non-standard scenario. It hints towards the possible
relaxation of the lower bound of the lightest right handed neutrino mass
required to produce adequate asymmetry which is in agreement with current
experimental data.
