What information about inflation could be gained from a measurement of the Cosmic Gravitational Wave Background? 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? 
 A: First of all inflation is more and idea than it is a concrete theory. 
With this I mean that inflation predicts that there must have been some epoch in which spacetime expanded faster than the propagation speed of information(= light speed). But any theory that does this is called an inflation theory. 
In practice there are many possible theories that give rise to this behavior and it would be incredibly valuable to be able to rule some out. This is where the detection of the gravitational background comes in. Every theory for inflation predicts that there will be some background in both the gravitation and thermal field. Moreover, they all predict some relative value of their intensities, this is the so called scalar to tensor ratio.
Measuring the cosmic gravitational background would tell us the exact value of this tensor to scalar ratio and with it exclude many modes for inflation bringing us one step closer to the correct model...
A: 
inflation as we understand it would have been very unlikely to produce the universe we now observe

Actually it's the opposite - without inflation it would be very unlikely to see the universe in this particular state, since we would have to tune the initial conditions. What inflation does is makes the predictions insensitive to initial conditions, and "hides" the initial singularity. 
Currently, all we have is purely phenomenological models of inflation from which we choose experimentally favorable ones (at the same time trying to derive those models from strings, developing supergravity extensions, etc.)
