Modular invariant inflation
  Modular invariance is a striking symmetry in string theory, which may keep
stringy corrections under control. In this paper, we investigate a
phenomenological consequence of the modular invariance, assuming that this
symmetry is preserved as well as in a four dimensional (4D) low energy
effective field theory. As a concrete setup, we consider a modulus field $T$
whose contribution in the 4D effective field theory remains invariant under the
modular transformation and study inflation drived by $T$. The modular
invariance restricts a possible form of the scalar potenntial. As a result,
large field models of inflation are hardly realized. Meanwhile, a small field
model of inflation can be still accomodated in this restricted setup. The
scalar potential traced during the slow-roll inflation mimics the hilltop
potential $V_{ht}$, but it also has a non-negligible deviation from $V_{ht}$.
Detecting the primordial gravitational waves predicted in this model is rather
challenging. Yet, we argue that it may be still possible to falsify this model
by combining the information in the reheating process which can be determined
self-completely in this setup.
