Very Hairy Inflation
  We revisit the rollercoaster cosmology based on multiple stages of monodromy
inflation. Working within the framework of effective flux monodromy field
theory, we include the full range of strong coupling corrections to the
inflaton sector. We find that flattened potentials $V \sim \phi^p + \ldots$
with $p \la 1/2$, limited to $ N \la 25 - 40$ efolds in the first stage of
inflation, continue to fit the CMB. They yield $0.96 \la n_s \la 0.97$, and
produce relic gravity waves with $0.006 \la r \la 0.035$, in full agreement
with the most recent bounds from BICEP/{\it Keck}. The nonlinear derivative
corrections generated by strong dynamics in EFT also lead to equilateral
non-Gaussianity $f_{NL}^{eq} \simeq {\cal O}(1) - {\cal O}(10)$, close to the
current observational bounds. Finally, in multi-stage rollercoaster, an
inflaton-hidden sector $U(1)$ coupling can produce a tachyonic chiral vector
background, which converts rapidly into tensors during the short interruption
by matter domination. The produced stochastic gravity waves are chiral, and so
they may be clearly identifiable by gravity wave instruments like LISA, Big
Bang Observatory, Einstein Telescope, NANOgrav or SKA, depending on the precise
model realization. We also point out that the current attempts to resolve the
$H_0$ tension using early dark energy generically raise $n_s$. This may
significantly alter the impact of BICEP/{\it Keck} data on models of inflation.
