1. Construct diagrams of expansion factor R versus time t to illustrate the evolution of the following universe models:
(a) A big bang universe in which the expansion rate is accelerating
(b) A big bang universe in which expansion is decelerating, leading to a contraction phase and a big crunch.
(c) A big bang universe which is expanding, and decelerating, but will not go back to a big crunch.
2. Assume that the Hubble constant is 70 kilometers per second per Megaparsec. Using the Hubble law and the nonrelativistic redshift formula, z = v/c where z is the redshift, calculate how far away a galaxy is if it has a redshift of one percent (z = 0.01). Note that the speed of light is 3×105 kilometers per second.