  We calculate the quadra-spectrum and quint-spectrum, corresponding to five
and six point correlation functions of the curvature perturbation. For single
field inflation with standard kinetic term, the quadra-spectrum and
quint-spectrum are small, which are suppressed by slow roll parameters. The
calculation can be generalized to multiple fields. When there is no entropy
perturbation, the quadra-spectrum and quint-spectrum are suppressed as well.
With the presence of entropy perturbation, the quadra-spectrum and
quint-spectrum can get boosted. We illustrate this boost in the multi-brid
inflation model. For the curvaton scenario, the quadra-spectrum and
quint-spectrum are also large in the small r limit. We also calculate
representative terms of quadra-spectrum and quint-spectrum for inflation with
generalized kinetic terms, and estimate their order of magnitude for
quasi-single field inflation.
