  We obtain axionic charged primordial black holes on a vacuum created
gravitational pair of $(3{\bar 3})$-brane by the Kalb-Ramond field on a
$D_4$-brane in presence of a background open string metric. The new geometries
on an emergent pair of $(3{\bar 3})$-brane universe is shown to be influenced
by the non-perturbative quantum effects underlying a geometric torsion in a
second order formalism. The presence of small extra dimensions transverse to
the pair in the formalism ensures dynamical scalar fields hidden to a $3$-brane
or an anti 3-brane universe. We investigate the non-perturbative quantum vacua
for their characteristic properties to explain the accelerated expansion of our
universe. Interestingly the emergent brane universe is shown to possess its
origin in a degenerate stringy de Sitter vacua at an early epoch. A
non-perturbative $D_p$-brane world volume correction for $p < 3$ is worked out
to explain some of the quantum effects underlying a quintessence axion in the
string-brane setup. Our analysis reveals that a $D$-instanton can be a
potential candidate to source the dark energy in our brane universe.
