Low-energy effects in a higher-derivative gravity model with real and complex massive poles

Abstract

The most simple superrenormalizable model of quantum gravity is based on the general local covariant six-derivative action. In addition to graviton such a theory has massive scalar and tensor modes. It was shown recently that in the case when the massive poles emerge in complex conjugate pairs, the theory has also unitary S-matrix and hence can be seen as a candidate to be a consistent quantum gravity theory. In the present work we construct the modified Newton potential and explore the gravitational light bending in a general six-derivative theory, including the most interesting case of complex massive poles. In the case of the light deflection the results are obtained within classical and semiclassical approaches.MSC: 53B50, 83D05, 81T20

On the gravitational seesaw in higher-derivative gravity

“…At quantum level it yields scattering cross-sections that depend on the energy of the photon, as was shown, e.g., in Refs. [20,21,39]. This result, however, has little application for the deflection by astronomical bodies [21].…”

“…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.…”

“…Let us note that these and related subjects are discussed in detail in the context of the general sixderivative model in the parallel paper [21]. Here we present just a brief extract of the results which have a relation to the seesaw mechanism.…”

“…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].…”

“…4. We remark that the main focus of this communication is on the seesaw mechanism, while the detailed discussion concerning phenomenological aspects of the theory with six or more derivatives of the metric will be given in the parallel work [21], devoted to the modified Newtonian potential and the bending of light. Finally, in Sect.…”