  We perform a comprehensive study on the role of thermal noise on the ordering
kinetics of a collection of active Brownian particles modeled using
coarse-grained conserved active model B (AMB). The ordering kinetics of the
system is studied for the critical mixture when quenched from high to a low
temperature. The structure of the growing domains changes from isolated droplet
type for AMB without noise to bi-continuous type for active model B with noise
(AMBN). Unlike the passive counterpart of the AMB, the noise is relevant for
the growth kinetics of the AMB. We use extensive numerical study, as well as
dynamic scaling hypothesis to characterize the kinetics of the system. We find
that the asymptotic growth law for AMBN is diffusive Lifshitz-Slyozov (LS)
type, whereas it was reported previously that the asymptotic growth law for the
AMB without noise is slower, with a growth exponent 4. Moreover, the kinetics
of the growing domains show a strong time dependent growth for AMBN. The growth
law shows a crossover from early time 1/3 value to intermediate time 1/4 value,
and it again traverses from 1/4 to 1/3 asymptotically. The two different
scaling functions are found for intermediate time and late time with growth law
1/4 and 1/3 respectively.
