I understand that inflation predicts that there is a primordial gravitational wave background due to quantum fluctuations in the gravitational field. Inflation is, of course, very important in terms of modern cosmology and it explains various things about the universe in which we live (homogeneity, isotropy, flatness, and the lack of magnetic monopoles).
However, there is a significantly sized group of scientists who aren't ok with the theory, I guess mostly due to theoretical considerations that would seem to imply that
a) inflation as we understand it would have been very unlikely to produce the universe we now observe - "Of all the ways the universe could have begun, only a tiny fraction would lead to the uniform, flat state observed today,"
b) the theory in some sense "predicts everything," and therefore predicts nothing. Inflation predicts an infinity of "bubbles," with an infinity of properties, always nucleating and growing in an eternal inflation on a scale larger than our observable universe.
So the theory of inflation is effective for explaining things we see, but ineffective in other ways. So my question is, in layman's terms, what information could we gain about the inflationary era by measuring the cosmic GW background? Conversely, what would be implied if (purely hypothetically) it was found that this background does not exist, or had a spectrum that was different from what we expect?