  We consider the possibility of realizing inflation in nonlocal field theories
containing infinitely many derivatives. Such constructions arise naturally in
string field theory and also in a number of toy models, such as the p-adic
string. After reviewing the complications (ghosts and instabilities) that arise
when working with high derivative theories we discuss the initial value problem
and perturbative stability of theories with infinitely many derivatives. Next,
we examine the inflationary dynamics and phenomenology of such theories.
Nonlocal inflation can proceed even when the potential is naively too steep and
generically predicts large nongaussianity in the Cosmic Microwave Background.
