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Topological Quintessence

A global monopole (or other topological defect) formed during a recent phase transition with core size comparable to the present Hubble scale, could induce the observed accelerating expansion of the universe. In such a model, topological considerations trap the scalar field close to a local maximum of its potential in a cosmologically large region of space. We perform detailed numerical simulations of such an inhomogeneous dark energy system (topological quintessence) minimally coupled to gravity, in a flat background of initially homogeneous matter. We find that when the energy density of the field in the monopole core starts dominating the background density, the spacetime in the core starts to accelerate its expansion in accordance to a ΛCDM model with an effective inhomogeneous spherical dark energy density parameter Ω_Λ(r). The matter density profile is found to respond to the global monopole profile via an anti-correlation (matter underdensity in the monopole core). Away from the monopole core, the spacetime is effectively Einstein-deSitter (Ω_Λ(r_{out}) -> 0) while at the center Ω_Λ(r ~ 0) is maximum. We fit the numerically obtained expansion rate at the monopole core to the