The study of gravitaional waves is an excellent way of determining the direction in which the universe is going i.e. Meaning whether the universe is slowing down or still expanding. This would be a break through in the idea that everything is slowing down and that there is some perpetual energy being created. That some how potential energy is being converted to kinetic energy through a means we have yet to understand.
The study of gravitational waves, originally postulated by Einstein 100 years ago, has now been proven to be correct. The study with the telescope in the South Pole proves without a doubt that inflation, or expanding universe is proven. The scientists are extremely conservative and would not be making this statement if it were not true.
The big bang has several models in which it explains why the universe is expanding today and how we have came to be since origins. The inflationary model is what the gravitational waves have helped verify. Previously we pretty much only had the cosmic wave background and a couple of measurements taken by the WMAP spacecraft and etc backing this theory. Now with gravitational waves, we have pretty much put the nail in the coffin and it's as valid a theory as evolution persay.
We've known that the universe is expanding because of general relativity and the hubble space telescope that has observed multiple galaxies accelerating away from us. The question is WHY it's expanding. That's where the new frontier is. People think it's because of dark energy.. Look it up.
I believe the study of gravitational waves can give us more information about our universe, but we already know that the universe is expanding. The breakthrough gave us more information about the rapid expansion that happened at first and gravitational waves can give us more information, but they're not going to drastically change any of our current theories.
No, I do not believe that the study of gravitational waves will prove that the universe is expanding, because we already do not know how far the universe goes. If there is no end to the universe in the first place, how can we prove that it expands anymore? It is a problem with the concept of infinity.