A mathematical quantity that describes the changing separation of two points as the Universe expands. It can be thought of as a time-dependent magnification factor. In the expanding Universe, separations between points increase uniformly so that a regular grid at some particular time looks like a blown-up version of the same grid at an earlier time. Because the symmetry is preserved, one needs to know only the factor by which the grid has been expanded in order to establish the past grid from the later one. Likewise, one needs to know only the scale factor to obtain a picture of the past physical conditions from present data.