Milne model

[1] It is mathematically equivalent to a special case of the FLRW model in the limit of zero energy density and it obeys the cosmological principle[citation needed].

Since it features both zero energy density and maximally negative spatial curvature, the Milne model is inconsistent with cosmological observations[citation needed].

The Milne solution can be obtained from the more generic FLRW model by demanding that the energy density, pressure and cosmological constant all equal zero and the spatial curvature is negative.

[citation needed] From these assumptions and the Friedmann equations it follows that the scale factor must depend on time coordinate linearly.

When rendered graphically Milne's density distribution shows a three-dimensional spherical Lobachevskian pattern with outer edges moving outward at the speed of light.

Milne's model follows the description from special relativity of an observable universe 's spacetime diagram containing past and future light cones along with "elsewhere" in spacetime.
Milne's model in comoving FLRW coordinates : the Hubble radius (blue) is at a constant comoving distance. The past and future light cone are depicted in orange, the Minkowskian hypersurface of the present in purple and the hypersurface of constant FLRW time in red.