Consider a universe with energy density u = uc, where uc is the critical density and 6= 1. Assume that we're discussing the present time (t = t0) and that the current value of the Hubble parameter is H0. This universe is described by the full version of the Relativistic Friedmann Equation (RFE) 1 a da dt !2 = 8 3 Gu(t) c 2 c2 R2 0a 2 , (4) with 6= 0. (a) Using the RFE, verify that is negative if < 1, and positive if > 1. (b) Fixing || = 1, use the RFE to derive an equation for the present value of the curvature scale R0. This is the length scale on which the curvature of a universe with 6= 1 is evident. (c) Suppose the universe is open, with = 0.3. Compare the curvature scale R0 to the distance to the "last scattering" surface, ct0 ' 4.24 Gpc