  We consider a contracting universe and its transition to expansion through
the big bang singularity with a time varying equation of state $w$, where $w$
approaches $1$ as the universe contracts to the big bang. We show that this
singularity is non-regularizable. That is, there is no unique extension of the
physical quantities after the transition, but rather infinitely many. This is
entirely different from the case of $w > 1$ studied in \cite{Xue:2014}, where
$w$ approaches a constant value $w_c > 1$ as the universe contracts. In that
case a continuous transition through the big bang to yield a unique extension
was possible only for a discrete set of $w_c$ satisfying coprime conditions. We
also show that there exists another time variable, $N$, at the big bang
singularity itself, at $t=0$, where $w$, varies as a function of $N$. This
defines an {\em extended big bang state}. Within it, $H$ is infinity. In the
extended state, $w$ varies from a universe dominated by the cosmological
constant to $1$. After $w$ reaches $1$ then the big bang occurs and time $t >0$
resumes. This gives a dynamical mechanism for the big bang that is
mathematically complete as a function of $N$. Dynamical systems methods are
used with classical modeling.
