Perturbative region on non-Gaussian parameter space in single-field
  inflation
  We calculate one-loop correction to the two-point functions of curvature
perturbation in single-field inflation generated by cubic self-interaction.
Incorporating the observed red-tilted spectrum of curvature perturbation, the
relevant one-loop correction takes a finite value and inversely proportional to
the spectral tilt. Requiring one-loop correction to be much smaller than the
tree-level contribution leads to an upper bound on primordial non-Gaussianity.
While observationally allowed region of non-Gaussian parameter space is found
to be entirely included by the region where one-loop correction is smaller than
the tree-level contribution, if we tighten the theoretical requirement to
require that the former should be smaller than, say, 10% or 1% of the latter,
significant parts of the observationally allowed region are ruled out. If
future observations conclude non-Gaussianity falls in such a region, then it
would be important to incorporate higher-order corrections to the spectrum in
order to achieve precise cosmology. In some extreme cases, it might indicate
breakdown of the cosmological perturbation theory in the context of
single-field inflation.
