We present a simple mechanism for obtaining largefield inflation,
and hence a gravitational wave signature, from string theory. They
basic structure involved in extending the field range  monodromies
in the presence of wrapped Dbranes combined with symmetries
protecting the flatness of an inflaton potential  arises in several
classes of string compactifications. In one example, type IIA string
theory on Nil manifolds with a spacetime filling D4brane moving
along an internal circle, we obtain a leading inflationary potential
proportional to phi^(2/3) in terms of the canonically normalized field
phi, yielding predictions for the tilt of the power spectrum and the
tensortoscalar ratio, n_s = 0.98 and r = 0.04 with 60 efoldings of
inflation. In a second example, wrapped branes can also introduce a
monodromy that extends the field range of individual closedstring
axions to beyond the Planck scale. Shift symmetries of the system
naturally control corrections to the axion potential. This suggests a
general mechanism for chaotic inflation driven by monodromyextended
closedstring axions. We systematically analyze this possibility and
show its compatibility with moduli stabilization in e.g. warped
CalabiYau manifolds. In this broad class of models, the potential is
linear in the canonical inflaton field, predicting a tensor to scalar
ratio r = 0.07 accessible to upcoming cosmic microwave background
(CMB) observations.
