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 \Lambda CDM model
with an effective inhomogeneous spherical dark energy density parameter
\Omega_\Lambda(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 (\Omega_\Lambda(r_{out}) -> 0) while at the center
\Omega_\Lambda(r ~ 0) is maximum. We fit the numerically obtained expansion
rate at the monopole core to the Union2 data and show that the quality of fit
is almost identical to that of \Lambda CDM. Finally, we discuss potential
observational signatures of this class of inhomogeneous dark energy models.
