  Type Ia supernovae (SNeIa), used as one of the standard candles in
astrophysics, are believed to form when the mass of the white dwarf approaches
Chandrasekhar mass limit. However, observations in last few decades detected
some peculiar SNeIa, which are predicted to be originating from white dwarfs of
mass much less than the Chandrasekhar mass limit or much higher than it.
Although the unification of these two sub-classes of SNeIa was attempted
earlier by our group, in this work, we, for the first time, explain this
phenomenon in terms of just one property of the white dwarf which is its
central density. Thereby we do not vary the fundamental parameters of the
underlying gravity model in the contrary to the earlier attempt. We effectively
consider higher order corrections to the Starobinsky-$f(R)$ gravity model to
reveal the unification. We show that the limiting mass of a white dwarf is
$\sim M_\odot$ for central density $\rho_c \sim 1.4\times10^8$ g/cc, while it
is $\sim 2.8M_\odot$ for $\rho_c \sim1.6\times 10^{10}$ g/cc under the same
model parameters. We further confirm that these models are viable with respect
to the solar system test. This perhaps enlightens very strongly the long
standing puzzle lying with the predicted variation of progenitor mass in SNeIa.
