"[T]o extend this to the geometry of spacetime... include a term... in the spacetime line element, with a now an arbitrary function of time (known as the Robertson-Walker scale factor):d\tau^2 \equiv -g_{\mu\nu}(x) dx^\mu dx^\nu = dt^2-a^2(t)[d\mathbf{x}^2 + K \frac{(\mathbf{x} \cdot d\mathbf{x}^2)}{1-K\mathbf{x}^2}]"