The robertson-walker metric is given by dr2 d. s2 -dt a(t) 1kr r(d02 + sin2 odo (iii the parameter k corresponds to the square of the inverse-radius of curvature. discuss the physical significance of: positive spatial curvature, i. e. k > 0; and negative spatial curvature, i. e. k < 0, with respect to the extent of the universe and the behaviour of parallel geodesics (iv) it is believed that our universe has approximately zero spatial curvature, i. e. k = 0. given this, write down an expression for the speed of radially propagating light in terms of the robertson-walker co-ordinates (v) given that a(t) is increasing with time, what does this light speed imply about the frequency of light observed from distant galaxies? to answer this question consider how long it takes for light to propagate a fixed co-ordinate distance dr in the present, and the same fixed co-ordinate distance at some time in the past. you can relate the time intervals obtained st*, to frequencies via w; 2n/dt; .