Unique contributions to the scalar bispectrum in `just enough inflation'

A scalar field rolling down a potential with a large initial velocity results in inflation of a finite duration. Such a scenario suppresses the scalar power on large scales improving the fit to the cosmological data. We find that the scenario leads to a hitherto unexplored situation wherein the boundary terms dominate the contributions to the scalar bispectrum over the bulk terms. We show that the consistency relation governing the non-Gaussianity parameter $f_{_{\rm NL}}$ is violated on large scales and that the contributions at the initial time can substantially enhance the value of $f_{_{\rm NL}}$.