Local Scale-Dependent Non-Gaussian Curvature Perturbations at Cubic Order

We calculate non-Gaussianities in the bispectrum and trispectrum arising from the cubic term in the local expansion of the scalar curvature perturbation. We compute to three-loop order and for general momenta. A procedure for evaluating the leading behavior of the resulting loop-integrals is developed and discussed. Finally, we survey unique non-linear signals which could arise from the cubic term in the squeezed limit. In particular, it is shown that loop corrections can cause $f_{NL}^{sq\mathrm{.}}$ to change sign as the momentum scale is varied. There also exists a momentum limit where ${\tau }_{NL}<0$ can be realized.