Problem 1 [5] (i) Compute the Christoffel symbol of the Friedmann-Robertson-Walker line element ds' = -dr' + a(r)?(d.x2 + dy? + dz?) with some function a(7). (Express your result in terms of a and a = da/dr.) (ii) Compute the Ricci tensor of the Friedmann-Robertson Walker line element. You may use the fact that it is diagonal in the given coordinates, and thanks to isotropy, obeys Rex = Ryy = Rizz. (iii) Show that the tt-component of Einstein's equation for a Friedmann- Robertson-Walker universe is equivalent to the Friedmann equation 2 8TG 3 P where the energy density p is the tt-component of the stress-energy tensor