3. During the first 380,000 years after the big bang, radiation interacted constantly with electric charges in the ambient plasma. The universe was expanding and cooling until, finally, neutral atoms formed, after which the photons stopped interacting with electrons and other charges. (So, the universe became essentially transparent to the radiation.) The time at which this occurred is known as the last scattering time. Those photons, which today constitute the CMB, have traveled for almost 13.8 billion years and reach us now from roughly the same distance which, from our perspective, determines a sphere surrounding us, whose surface is called the last scattering surface. Assume the ACDM model is correct, and that the redshift of the last scattering surface is & = 1,090. (a) (6 pts) What is the proper distance d to the surface of last scattering? (This is the radius of the spherical region mentioned above.) (b) (2 pts) What is the luminosity distance d, to the surface of last scattering? (c) (2 pts) What about the angular-diameter distance