A period of exponentially fast expansion in the early Universe -- inflation -- solves several cosmological puzzles, and potentially links quantum gravity with cosmological observations. General expectations from a quantum theory of gravity include the "Weak Gravity Conjecture", which roughly states that gravity is the weakest force. I will discuss what this conjecture implies for an interesting class of inflationary models called "large field inflation", which predict that primordial gravitational waves that could be observed in the near future.