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

Abstract

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 ${r}_{0\mathrm{min}}$ of such a dark energy inhomogeneity that is consistent with the Union2 type Ia supernovae data at the $3\ensuremath{\sigma}$ level is ${r}_{0\mathrm{min}}\ensuremath{\simeq}1.8\text{ }\text{ }\mathrm{Gpc}$. As expected, the best-fit fractional dark energy density at the center, ${\ensuremath{\Omega}}_{X,\mathrm{in}}$, approaches the corresponding $\ensuremath{\Lambda}\mathrm{CDM}$ value ${\ensuremath{\Omega}}_{X,\mathrm{in}}=0.73$ for large enough values of the inhomogeneity radius ${r}_{0}$ (${r}_{0}>4\text{ }\text{ }\mathrm{Gpc}$). Using the Union2 data, we show that the maximum allowed shift ${r}_{\mathrm{obs}\mathrm{\text{\ensuremath{-}}}\mathrm{max}}$ of the observer from the center of the inhomogeneity is about $0.7{r}_{0}$, 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 ${r}_{\mathrm{obs}\mathrm{\text{\ensuremath{-}}}\mathrm{max}}$ coming from the magnitude of the CMB dipole remain a severe challenge to the Copernican principle and lead to ${r}_{\mathrm{obs}\mathrm{\text{\ensuremath{-}}}\mathrm{max}}<110\text{ }\text{ }\mathrm{Mpc}$, even for an inhomogeneity radius as large as ${r}_{0}=7\text{ }\text{ }\mathrm{Gpc}$.