where (r, θ, φ) correspond to a spherical coordinate system. This metric has only two undetermined parameters. An overall dimensionless length scale factor R describes the size scale of the universe as a function of time (an increase in R is the expansion of the universe), and a curvature index k describes the geometry. The index k is defined so that it can take only one of three values: 0, corresponding to flat Euclidean geometry ; 1, corresponding to a space of positive curvature ; or −1, corresponding to a space of positive or negative curvature. The value of R as a function of time t depends upon k and the cosmological constant Λ. The cosmological constant represents the energy density of the vacuum of space and could be related to dark energy. The equation describing how R varies with time is known as the Friedmann equation after its inventor, Alexander Friedmann.