1. [20 points total] We learned in class that the proper distance at any time 1, (t) is equal to the comoving distance,

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1 20 Points Total We Learned In Class That The Proper Distance At Any Time 1 T Is Equal To The Comoving Distance 1 (95.3 KiB) Viewed 35 times

1. [20 points total] We learned in class that the proper distance at any time 1, (t) is equal to the comoving distance, r, times the scale factor a at that time: ep(t) = a(t)r, and that the current proper time, (o) is equal to the current comoving time, ep(to) = r. A) [10 pts] Assuming the total baryonic mass of the Universe remains constant, show that this implies the baryon density at any time t is given by: Po,b Pb(t) = a(t)3 where Pob is the baryon density at t= to. Hint: Calculate the baryon density in an arbitrary volume. B) [10 pts] WMAP calculates the current density of baryons in the Universe as Po,b= 4.17 x 10-28 kg m-³. Given that the current 4 temperature of the Universe is To = 2.73 K, what was the baryon density, Ph, when the Universe had a temperature T = 10¹⁰K? Recall that T 1/a. ~