Among the so-called classical tests of general relativity (GR), light bending has been confirmed with an accuracy that increases as times goes by. Here we study the gravitational deflection of photons within the framework of classical and semiclassical higher-derivative gravity (HDG) -the only version of GR that is known up to now to be renormalizable along with its matter couplings. Since our computations are restricted to scales much below the Planck cut-off we need not be afraid of the massive spin-2 ghost that haunts HDG. An upper bound on the constant related to the R 2 µν -sector of the theory is then found by analyzing -from a classical and semiclassical viewpoint -the deflection angle of a photon passing by the Sun. This upper limit greatly improves that available in the literature.

A straightforward prescription for computing the D-dimensional potential energy of gravitational models, which is strongly based on the Feynman path integral, is built up. Using this method, the static potential energy for the interaction of two masses is found in the context of D-dimensional higher-derivative gravity models, and its behavior is analyzed afterwards in both ultraviolet and infrared regimes. As a consequence, two new gravity systems in which the potential energy is finite at the origin, respectively, in D = 5 and D = 6, are found. Since the aforementioned prescription is equivalent to that based on the marriage between quantum mechanics (to leading order, i.e., in the first Born approximation) and the nonrelativistic limit of quantum field theory, and bearing in mind that the latter relies basically on the calculation of the nonrelativistic Feynman amplitude ( ), a trivial expression for computing is obtained from our prescription as an added bonus.

In this work we investigate an interesting connection between the absence of Newtonian singularities in the classical non-relativistic potential and renormalizability properties in Higher-Derivative models of Quantum Gravity. In the framework of a large class of Ddimensional Higher-Derivative models of Quantum Gravity, we compute the non-relativistic potential energy associated with two point-like masses. Investigating its behavior for small distances, we find an algebraic condition which is sufficient for the cancellation of the Newtonian singularity. We verify that the same condition is necessary to ensure power-counting renormalizability and, as a consequence, we conclude that renormalizable Higher-Derivative models do not exhibit the so-called newtonian singularity. Finally, we discuss the role of ghosts in the mechanism for the cancellation of Newtonian singularities. I. INTRODUCTIONThe quest for a quantum gravity theory is still one of the most important problems of theoretical physics. As is well known, the biggest challenge in the construction of a quantum theory for the gravitational interaction is the lack of experimental evidences concerning gravity at the microscopic level. Despite that, however, there exist several approaches to quantum gravity which were proposed in the last few decades. For instance: string theory, loop quantum gravity, causal dynamical triangulations, causal sets and induced quantum gravity [1,2]. Nevertheless, none of the aforementioned theories can be considered a complete quantum gravity theory up to now.At the classical level, the gravitational interaction is very well described in terms of Einstein's general relativity (GR), which is confirmed for the excellent concordance between its theoretical predictions and the available experimental tests (e.g.

The deflection of any particle by an external weak gravitational field in the framework of Einstein’s general relativity (which is a geometrical theory) is, of course, non-dispersive. Nonetheless, things are completely different if the deflection is studied within the context of semiclassical gravity (or tree-level gravity). Indeed, to first order the cross sections corresponding to the scattering of different quantum particles by a weak gravity field, treated as an external field, as well as the related bending angles, are spin dependent, while to second order the deflection is dispersive (energy dependent). Interestingly enough, in the framework of semiclassical higher-derivative gravity the bending is already energy dependent to first order. In this paper we discuss these disagreements between quantum mechanics and the equivalence principle.

Simple prescriptions for computing the D-dimensional classical potential related to electromagnetic and gravitational models, based on the functional generator, are built out. These recipes are employed afterward as a support for probing the premise that renormalizable higher-order systems have a finite classical potential at the origin. It is also shown that the opposite of the conjecture above is not true. In other words, if a higher-order model is renormalizable, it is necessarily endowed with a finite classical potential at the origin, but the reverse of this statement is untrue. The systems used to check the conjecture were D-dimensional fourth-order Lee–Wick electrodynamics, and the D-dimensional fourth- and sixth-order gravity models. A special attention is devoted to New Massive Gravity (NMG) since it was the analysis of this model that inspired our surmise. In particular, we made use of our premise to resolve trivially the issue of the renormalizability of NMG, which was initially considered to be renormalizable, but it was shown some years later to be non-renormalizable. We remark that our analysis is restricted to local models in which the propagator has simple and real poles.