Higher-order regularity in local and nonlocal quantum gravity

Abstract In the present work we investigate Newtonian limit of higher-derivative gravity theories with more than four derivatives in action, including non-analytic logarithmic terms resulting from one-loop quantum corrections. The first part paper deals occurrence curvature singularities metric classical models. It is shown that case local theories, even though scalars are regular, invariants involving curvatures can still diverge. Indeed, prove if action contains $$2n+6$$ 2 n + 6 both scalar and spin-2 sectors, then all curvature-derivative at most 2 n covariant while there exist $$2n+2$$ singular. regularity these be achieved some classes nonlocal theories. second paper, show leading corrections do not change limit. Finally, also consider infrared solutions verify universality correction to potential investigated paper.