I'm not saying that the inflationary phase of the universe is a false concept, but I've always thought that the way the theory came about is a bit sketchy.
Please correct me if I'm mistaken with any of this, but this is my understanding of its history. Earlier versions of the Big Bang theory did not include this rapid inflation in the earlier universe; the universe was said to expand at a more constant rate. However, when the Cosmic Microwave Background Radiation was first observed, there was no way to explain its irregularity based on that model. So physicists decided to plunk down a mysterious inflationary phase into their models of the early universe, a concept with no known cause or explanation, but which made the CMBR fit with the Big Bang theory. However, it's a concept that to this day they're still trying to reconcile with the rest of observed physics, as this article shows.
Could the theory be true? Sure. But if it is, it's because those physicists got lucky with their educated guess on the matter. Other theories with much more solid backing have in the past been roundly disproven.