Monodromy inflation at strong coupling: $4\pi$ in the sky
  We present a simple effective field theory formulation of a general family of
single field flux monodromy models for which strong coupling effects at large
field values can flatten the potential and activate operators with higher
powers of derivatives. These models are radiatively and non-perturbatively
stable and can easily sustain $\ga 60$ efolds of inflation. The dynamics
combines features of both large field chaotic inflation and $k$-inflation, both
of which can suppress the tensor amplitude. Reducing the tensor-scalar ratio
below the observational bound $r \lesssim 0.1$ while keeping the scalar
spectral index $n_s$ within experimental bounds either yields equilateral
nongaussianity $f_{NL}^{eq} \simeq {\cal O}(1)$, close to the current
observational bounds, or ultimately gives very small $r$.
