{h} [2.[lpt]: Let's continue to study a universe that contains only,r one uid with an equation of state equal to w 3::- 1. Show that the comoving proper distance. D, of a galaxy that we observe today and that emitted its photons at a scale factor of emission, oi\" is given by 3ct' + w) '1 H W T d ln(o) (35 I 1'":ch Solve this integral with the assumption that w 7E 1.33. Last. show that if D: w 2* \"3. then the comoving distance tends. in the limit a :r oo, to 3cr(1 + w) D ;. . So, if the Universe is decelerating, there is always a (l + 3w) horizon. Le. a maximum comoving distance where the light from galaxies can reach us. '3' a 1m) HINT: Remember that D = {we found that on HW4). Inter] [1H