Isotropic Expansion of Inhomogeneous Universe

We propose a cosmological model that describes isotropic expansion of inhomogeneous universe. The energy-momentum tensor that creates the spatial inhomogeneity may not affect the uniform expansion scaling factor $a(t)$ in the FLRW-like metrics. Such energy-momentum tensor may not be exotic; in fact any linear or non-linear $\sigma$-model has this feature. We show that the classical spatial inhomogeneity can be embedded in both inflation models and the traditional cosmological expansion by perfect fluid. The spatial inhomogeneity resembles the primordial quantum perturbation that was frozen in the co-moving frame. We obtain some exact inhomogeneous solutions with spherical or axial symmetries. We also show that some of our cosmological models can be viewed as the dynamical black hole formation.