On non-gaussianities in single-field inflation

TL;DR

This paper investigates how higher-dimension derivative operators, rooted in an approximate shift symmetry for the inflaton, can modify non-Gaussianities in single-field inflation. By focusing on the leading operator $\,(\nabla\phi)^4/M^4$, it demonstrates through a full bispectrum calculation that the resulting three-point function has a distinct angular dependence and a squeezed-limit suppression $\propto k_3^2$, while equilateral configurations yield $f_{\rm NL}^{\rm equil.} = {35\over108}{\dot\phi^2\over M^4}$. The analysis shows that, to maintain a valid EFT, $\dot\phi/M^2 \lesssim 1$, which in turn constrains $f_{\rm NL}$ to be at most of order unity, near the reach of Planck sensitivity. These results provide a concrete upper bound on non-Gaussian signals from single-field models and highlight a distinctive angular pattern as a potential discriminant from other sources of non-Gaussianity.

Abstract

We study the impact of higher dimension operators in the inflaton Lagrangian on the non-gaussianity of the scalar spectrum. These terms can strongly enhance the effect without spoiling slow-roll, though it is difficult to exceed f_NL ~ 1, because the scale which suppresses the operators cannot be too low, if we want the effective field theory description to make sense. In particular we explicitly calculate the 3-point function given by an higher derivative interaction of the form (\nablaφ)^4, which is expected to give the most important contribution. The angular dependence of the result turns out to be quite different from the minimal case without higher dimension operators.