On the cancellation of Newtonian singularities in higher-derivative gravity

Abstract

Recently there has been a growing interest in quantum gravity theories with more than four derivatives, including both their quantum and classical aspects. In this work we extend the recent results concerning the non-singularity of the modified Newtonian potential to the most relevant case in which the propagator has complex poles. The model we consider is Einstein-Hilbert action augmented by curvature-squared higher-derivative terms which contain polynomials on the d'Alembert operator. We show that the classical potential of these theories is a real quantity and it is regular at the origin despite the (complex or real) nature or the multiplicity of the massive poles. The expression for the potential is explicitly derived for some interesting particular cases. Finally, the issue of the mechanism behind the cancellation of the singularity is discussed; specifically we argue that the regularity of the potential can hold even if the number of massive tensor modes and scalar ones is not the same.

On the gravitational seesaw in higher-derivative gravity

“…Thus, only the weak seesaw is possible even in the model with complex poles. Further investigations on general higher-derivative models with complex poles are carried out in [23].…”

“…It is possible to show that, introducing a suitable gauge condition, the weak gravitational field generated by a static point-like mass, T μν (r) = Mη μ0 η ν0 δ (3) (r), has non-zero components given by (more detailed and general results are found in [22,23])…”

“…Indeed, the quantities μ 0± and μ 2± could be complex and still yield a real solution to the equations of motion (4) and thus physically admissible results, e.g., through a real effective potential [21,23]. Here, however, we restrict the analysis to the case of real poles, while the scenario with complex poles is explored in the following section.…”

“…This would imply, for example, modifications of Newton's inverse-square force law [21][22][23] which is measured in torsion-balance experiments [28,29]. In the case of complex poles for example, the corrections owed to the higher derivatives assume the form of oscillating terms as was noticed in [21,30].…”

Renormalizability, van Dam-Veltman-Zakharov discontinuity, and Newtonian singularity in higher-derivative gravity

“…In this case, a massive ghost tensor and a massive healthy scalar contribute in such a manner to cancel out the Newtonian singularity of a massless tensor. Recently, it was conjectured that the reverse of the above statement is not true, which indicates that the finiteness of the Newtonian potential at the origin is a necessary but not sufficient condition for the renormalizability of the model [4,5]. The model used in [5,6] includes a massive ghost tensor, massive ghost and heathy scalars in addition to a healthy tensor.…”