This, to Milne, was a deficiency inherent in the competing cosmological models which relied on the cosmological principle that demanded a homogeneous universe.

WMAP indicates (Figure 1) a smooth, homogeneous universe with density anisotropies of 10 parts per million.

In general relativity and inhomogeneous cosmology, the Kantowski-Sachs metric describes a homogeneous but anisotropic universe whose spatial section has the topology of .

It was soon understood that a homogeneous and isotropic universe could not be preserved through the violent tunneling process.

There are two independent Friedmann equations for modeling a homogeneous, isotropic universe.

Cosmologists were relieved that the spacecraft produced clear confirmation of the extremely smooth and homogeneous early universe, as predicted by Big Bang theory.

The Friedmann equations are derived by inserting the metric for a homogeneous and isotropic universe into Einstein's field equations for a fluid with a given density and pressure.

The homogeneous and isotropic universe allows for a spatial geometry with a constant curvature.

A homogeneous, isotropic universe does not have a center.

In 1923, Alexander Friedmann set out a variant of Einstein's equations of general relativity that describe the dynamics of a homogeneous isotropic universe.