I think it is correct. It explains many puzzling properties of our universe, and its predictions agree perfectly with current observations. However, it is not perfect or even complete. The theory says that very early on, the the universe had a very high vacuum energy density, which made the universe accelerate its expansion. We do not know what caused this energy density, and why it suddenly disappeared causing inflation to end. There are many theories but none of them is particularly convincing.
My own research deals with this particular problem. I try to calculate what happened at the end of inflation and find ways to test it observationally, so that we could then figure out what caused inflation.
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