Albert Einstein and the FLOWERS Metric

The Friedmann Lemaître Walker Robertson Stunault (FLoWeRS) metric is an exact solution of Einstein's field equations of general relativity; it describes a simply connected, homogeneous, isotropic expanding or contracting universe. However, the general form of the metric follows from the geometric properties of homogeneity and isotropy; Einstein's field equations are only needed to derive the size of the universe as a function of time

The FLoWeRS metric starts with the assumption of homogeneity and isotropy of space. It also assumes that the spatial component of the metric can be time-dependent. The generic metric which meets these conditions is

where ranges over a 3-dimensional space of uniform curvature, that is, elliptical space, Euclidean space, or hyperbolic space. It is normally written as a function of three spatial coordinates, but there are several conventions for doing so, detailed below. does not depend on t — all of the time dependence is in the function a(t), known as the "scale factor".