Isotropic Expansion of Inhomogeneous Universe

TL;DR

This paper introduces a cosmological model where inhomogeneous universes expand isotropically, integrating spatial inhomogeneity into standard cosmological frameworks without affecting the overall expansion rate.

Contribution

It presents a novel approach to modeling inhomogeneous universes with isotropic expansion, using energy-momentum tensors from sigma-models compatible with FLRW-like metrics.

Findings

Embedded inhomogeneity in inflation and cosmological models

Exact solutions with spherical or axial symmetry

Models resembling dynamical black hole formation

Abstract

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.