  In this Letter, we discuss the dynamics of a domain wall universe embedded
into the charged black hole spacetime of the Einstein-Born-Infeld (EBI) theory.
There are four kinds of possible spacetime structures, i.e., those with no
horizon, the extremal one, those with two horizons (as the
Reissner-Nordstr$\rm{\ddot o}$m black hole), and those with a single horizon
(as the Schwarzshild black hole). We derive the effective cosmological
equations on the wall. In contrast to the previous works, we take the
contribution of the electrostatic energy on the wall into account. By examining
the properties of the effective potential, we find that a bounce can always
happen outside the (outer) horizon. For larger masses of the black hole, the
height of the barrier between the horizon and bouncing point in the effective
potential becomes smaller, leading to longer time scales of bouncing process.
These results are compared with those in the previous works.
