Milne model

The Milne model was a special-relativistic cosmological model of the universe proposed by Edward Arthur Milne in 1935. 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]}. The Milne model is also similar to Rindler space in that both are simple re-parameterizations of flat Minkowski space.

Since it features both zero energy density and maximally negative spatial curvature, the Milne model is inconsistent with cosmological observations^{[citation needed]}. Cosmologists actually observe the universe's density parameter to be consistent with unity and its curvature to be consistent with flatness.

The Milne universe is a special case of a more general Friedmann–Lemaître–Robertson–Walker model (FLRW). 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.

Setting the spatial curvature and speed of light to unity the metric for a Milne universe can be expressed with hyperspherical coordinates as:

where

is the metric for a two-sphere and

is the curvature-corrected radial component for negatively curved space that varies between 0 and ${\displaystyle +\infty }$.

The empty space that the Milne model describes^{[citation needed]} can be identified with the inside of a light cone of an event in Minkowski space by a change of coordinates.