Quintessence and effective RN de Sitter brane geometries

We revisit an effective space-time torsion curvature in a second order formalism, underlying the non-linear $U(1)$ gauge dynamics, of a two form on a $D_4$-brane in type IIA superstring theory. The formalism incorporates the significance of a global NS two form into the theory via its perturbative coupling to a dynamical two form. In particular, we explore the non-linear gauge dynamics on a $D_4$-brane in presence of a non-trivial background metric. The fact that the global modes of a NS two form in an open string theory sources the background metric on a $D_4$-brane may hint at the existence of an anti $D_4$-brane in the formalism. An effective de Sitter universe is shown to emerge on a vacuum created pair of $(D{\bar D})_3$-brane by a local two form at the past horizon with a Big Bang. We obtain a number of 4D de Sitter quantum black holes, including a Reissner-Nordstrom vacuum, with and without a propagating torsion. The quantum black holes are shown to be free from curvature singularity at $r\rightarrow 0$. In a low energy limit, the nonperturbative correction sourced by a torison may seen to be insignificant. The quantum black hole undergoes an expansion in the limit and presumably identifies with the Einstein vacuum. Interestingly our analysis reveals a plausible quintessence (axion) on an anti $D_3$-brane which may source the dark energy in a $D_3$-brane universe. Arguably a brane universe moves away from its anti-brane due to the conjectured repulsive gravity underlying the quintessence. It leads to a growth in extra fifth dimension between a brane and an anti-brane which may provide a clue behind an accelerating universe observed in cosmology.