Generalized Lemaître-Tolman-Bondi model with inhomogeneous isotropic dark energy: Observational constraints

We consider on-center and off-center observers in an inhomogeneous, spherically symmetric, isocurvature (flat) concentration of dark energy with a typical size of a few Gpc. Such a concentration could be produced e.g. by a recently formed global monopole with core size that approaches the Hubble scale. In this case we would have what may be called ``topological quintessence'' in analogy with the well-known topological inflation. We show that the minimum comoving radius r0min of such a dark energy inhomogeneity that is consistent with the Union2 type Ia supernovae data at the 3σ level is r0min1.8 Gpc. As expected, the best-fit fractional dark energy density at the center, ΩX,in, approaches the corresponding ΛCDM value ΩX,in=0.73 for large enough values of the inhomogeneity radius r₀ (r₀>4 Gpc). Using the Union2 data, we show that the maximum allowed shift r_obs-max of the observer from the center of the inhomogeneity is about 0.7r₀, which respects the Copernican principle. The model naturally predicts the existence of a preferred axis and alignment of the low CMB multipoles. However, the constraints on r_obs-max coming from the magnitude of the CMB dipole remain a severe challenge to the Copernican principle and lead to r_obs-max<110 Mpc, even for an inhomogeneity radius as large as r₀=7 Gpc.