Lyth bound revisited
  Imposing that the excursion distance of inflaton in field space during
inflation be less than the Planck scale, we derive an upper bound on the
tensor-to-scalar ratio at the CMB scales, i.e. $r_{*,max}$, in the general
canonical single-field slow-roll inflation model, in particular the model with
non-negligible running of the spectral index $\alpha_s$ and/or the running of
running $\beta_s$. We find that $r_{*,max}\simeq 7\times 10^{-4}$ for
$n_s=0.9645$ without running and running of running, and $r_{*,max}$ is
significantly relaxed to the order of ${\cal O}(10^{-2}\sim 10^{-1})$ in the
inflation model with $\alpha_s$ and/or $\beta_s\sim +{\cal O}(10^{-2})$ which
are marginally preferred by the Planck 2015 data.
