Inflating with Large Effective Fields
  We re-examine large scalar fields within effective field theory, in
particular focussing on the issues raised by their use in inflationary models
(as suggested by BICEP2 to obtain primordial tensor modes). We argue that when
the large-field and low-energy regimes coincide the scalar dynamics is most
effectively described in terms of an asymptotic large-field expansion whose
form can be dictated by approximate symmetries, which also help control the
size of quantum corrections. We discuss several possible symmetries that can
achieve this, including pseudo-Goldstone inflatons characterized by a coset
$G/H$ (based on abelian and non-abelian, compact and non-compact symmetries),
as well as symmetries that are intrinsically higher dimensional. Besides the
usual trigonometric potentials of Natural Inflation we also find in this way
simple {\em large-field} power laws (like $V \propto \phi^2$) and exponential
potentials, $V(\phi) = \sum_{k} V_k \; e^{-k \phi/M}$. Both of these can
describe the data well and give slow-roll inflation for large fields without
the need for a precise balancing of terms in the potential. The exponential
potentials achieve large $r$ through the limit $|\eta| \ll \epsilon$ and so
predict $r \simeq \frac83(1-n_s)$; consequently $n_s \simeq 0.96$ gives $r
\simeq 0.11$ but not much larger (and so could be ruled out as measurements on
$r$ and $n_s$ improve). We examine the naturalness issues for these models and
give simple examples where symmetries protect these forms, using both
pseudo-Goldstone inflatons (with non-abelian non-compact shift symmetries
following familiar techniques from chiral perturbation theory) and
extra-dimensional models.
