(b) An observer at " = 0 and comoving time to receives a radial light signal (i.e., one that obeys dr- = 0 with r varying with t, and with # and $ fixed) sent at comoving time to from a source at distance r, from the observer. If the light is propagating in a Robertson-Walker geometry, find a relation between 1, to, to and R(t) for & positive, zero or negative. If the cosmology is described by a radiation fluid and the geometry has * = 0, determine how R(t) depends on t. For this particular R(t) determine the largest value of ", from which a signal can reach the observer