Answer
See answers.
Work Step by Step
a. We observe a redshift in the spectra of astronomical objects, providing direct evidence that all distant objects in the universe are moving away from one another. The farther the object, the faster its speed, so the universe is expanding. The expansion must have started at a point.
As discussed in section 33-6, the Big Bang theory predicted and explained the presence of cosmic microwave background radiation.
As discussed in section 33-7, the Big Bang theory explains the observed $25\%$ abundance of He in the universe.
b. The curvature of the universe affects its destiny because the curvature determines whether the universe is open (continue expanding forever) or closed (eventually stop expanding, and collapse).
c. Dark energy affects the future of the universe because its presence seems to have a long-range repulsive effect on space itself, causing an acceleration in the rate of expansion. This increases the probability that the universe is open.
