Quintessence and effective RN de Sitter brane geometries

Abstract

We revisit the 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. The formalism incorporates a significant 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 the presence of a non-trivial background metric. An effective de Sitter universe is shown to emerge on a vacuum created pair of $$(D{\bar{D}})_3$$ -branes by a local two form at the past horizon with the Big Bang. We obtain a number of $$4D$$ de Sitter quantum black holes with and without a propagating torsion. In a low energy limit the non-perturbative correction may be seen to be insignificant. The quantum black hole undergoes an expansion in the limit and 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 the extra fifth dimension between a brane and an anti-brane, which may provide a clue to an accelerating universe as observed in cosmology.