Cosmic inflation in non-perturbative quantum gravity

String field theory motivated infinite-derivative models lead to non-local gravity modifications which form a promising class of quantum gravity candidates. In this paper we investigate effects of non-locality on the three-point function (the bi-spectrum) during cosmic inflation. The study is done in an Einstein frame with an infinite-derivative scalar field Lagrangian minimally coupled to the Einstein-Hilbert term. A non-local generalization of the Mukhanov-Sasaki equation is derived. Infinite-derivative operators present in this equation lead to an appearance of infinitely many new background induced states in the perturbation spectrum during inflation with complex masses on top of a usual nearly massless inflaton. On contrary to a flat background such states can be classically stable in a de Sitter space-time. This helps preserving observational constraints on the scalar power-spectrum. We proceed by studying a particular configuration assuming that the generalized Mukhanov-Sasaki equation gives rise to an inflaton and one pair of new states with complex conjugate masses as perturbative degrees of freedom. The corresponding scalar bi-spectrum is computed numerically in squeezed and equilateral limits. We use the latest observational constraints on amplitude of the bi-spectrum $f_{NL}$ from Planck 2018 dataset as a guideline for possible values of masses of new emerging states. We find that $f_{NL}$ is non-trivially sensitive to the values of complex masses and this can reduce the parameter space of gravity modifications. In particular we find that the amplitude of the squeezed limit gets easily enhanced while of the equilateral limit can stay like in a local single-field model of inflation. We end up discussing open questions relevant for this class of models of inflation.