 In the 1920s and 1930s, a number of cosmological models of general relativity were proposed that predict the expansion of the universe. The most accurate account of the data is given by the family of Friedmann-Robertson-Walker (FRW) models. The key characteristic of these models is that space is homogeneous, and hence isotropic (i.e. looks the same in all directions). From the homogeneity assumption, it follows that the entire 4-dimensional spacetime divides neatly into a stack of 3-dimensional “spaces” each of which has constant curvature. The three possibilities for this curvature correspond to the three classical geometries: Euclidean (flat), spherical (positive), or hyperbolic (negative). In a given FRW spacetime, the geometry of space at one time is related to the geometry at any other time by means of a scale factor S(t). Indeed, pick a reference time T, such as 2021, pick two reference galaxies, and let d(T) be the distance between these galaxies at time T. Then the distance between the two galaxies at any other time t is given by d(t)=S(t)d(T), where we set S(T)=1. This number S(t) is called the scale factor, and its behavior encodes the dynamics of a FRW universe.