Higher-order regularity in local and nonlocal quantum gravity

TL;DR

This paper explores the Newtonian limit of higher-derivative and nonlocal quantum gravity theories, analyzing curvature singularities, the impact of quantum corrections, and the universality of quantum effects on gravitational potential.

Contribution

It provides a detailed analysis of curvature invariants and singularities in higher-derivative gravity, including the effects of quantum corrections and nonlocal modifications.

Findings

Curvature invariants involving derivatives can diverge even if scalars are regular.

Higher-derivative terms can regularize certain curvature-derivative invariants.

Quantum corrections do not alter the regularity of the Newtonian limit.

Abstract

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. The regularity of all these invariants can be achieved in some classes of nonlocal gravity theories. In the second part of the paper, we show that the leading logarithmic quantum corrections do not change the regularity of the Newtonian limit. Finally, we also consider the infrared limit of these solutions and verify the universality of the leading quantum correction to the potential in all the theories investigated in the paper.