  Cosmic Inflation provides an attractive framework for understanding the early
universe and the cosmic microwave background. It can readily involve energies
close to the scale at which Quantum Gravity effects become important. General
considerations of black hole quantum mechanics suggest nontrivial constraints
on any effective field theory model of inflation that emerges as a low-energy
limit of quantum gravity, in particular the constraint of the Weak Gravity
Conjecture. We show that higher-dimensional gauge and gravitational dynamics
can elegantly satisfy these constraints and lead to a viable,
theoretically-controlled and predictive class of Natural Inflation models.
