Higher-order regularity in local and nonlocal quantum gravity

Understand

In the present work we investigate the Newtonian limit of higher-derivative gravity theories with more than four derivatives in the action, including the non-analytic logarithmic terms resulting from one-loop quantum corrections.

• The first part of the paper deals with the occurrence of curvature singularities of the metric in the classical models.
• It is shown that in the case of local theories, even though the curvature scalars of the metric are regular, invariants involving derivatives of curvatures can still diverge.
• Indeed, we prove that if the action contains $2n+6$ derivatives of the metric in both the scalar and the spin-2 sectors, then all the curvature-derivative invariants with at most $2n$ covariant derivatives of the curvatures are regular, while there exist scalars with $2n+2$ derivatives that are singular.