In this paper we apply the usual perturbative methodology to evaluate the one-loop effective potential in a nonlocal scalar field theory. We find that the effect induced by the nonlocality of the theory is always very small and we discuss the consequences of this result. In particular we argue that, looking at one-loop corrections for matter fields, it is not possible to find signals of the nonlocality of the theory in cosmological observables since, even during inflation when energies are very high, nonlocality-induced corrections are expected to be very small.
Briscese, F., De Mello, E.R.B., Petrov, A.Y., Bezerra, V.B. (2015). One-loop effective potential in nonlocal scalar field models. PHYSICAL REVIEW D, PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY, 92(10) [10.1103/PhysRevD.92.104026].