One-loop effective potential in nonlocal scalar field models

TL;DR

This paper calculates the one-loop effective potential in nonlocal scalar field theories and finds that nonlocal effects are negligible, implying they are unlikely to produce observable signals in cosmology.

Contribution

It provides a perturbative evaluation of the one-loop effective potential in nonlocal scalar fields and demonstrates the smallness of nonlocal effects.

Findings

Nonlocality effects are very small in the effective potential.

One-loop corrections do not produce observable signals during inflation.

Nonlocality-induced corrections are negligible even at high energies.

Abstract

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 nonlocaliity 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.