3) (10 points) The cosmic microwave background (CMB) has a measured...

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3) (10 points) The cosmic microwave background (CMB) has a measured temperature of 2.73K but is radiation from the time of recombination (z = 1100) when the Universe was 3000 K. It can be modelled as arising from a sphere with a radius of 14.1 Gpc. a) (3 points) The primordial large-scale structure (i.e. scales much larger than individual galaxies) in the CMB (and, thus, in today's Universe) is best characterized by the acoustic peaks in the multipole diagram. Using this diagram (in our notes or Fig 8.14 in the text), calculate the radius of structures corresponding to the first 3 acoustic peaks in both today's universe (in Mpc), and at the time of recombination (in kpc) b) (4 points) If the Universe is flat, calculate the average density of the universe today and at the time of recombination (in kg Also, calculate the average mass (in Mo) contained within regions whose sizes correspond to the first 3 acoustic peaks. c) (3 points) The temperature fluctuations seen in the CMB are also best characterized by the acoustic peaks in the multipole diagram. Again, using this diagram, calculate the density fluctuations in the Universe (in kg m-3) in the first 3 acoustic peaks at the time of recombination. What are the % deviations from the mean density of the Universe?

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