Interesting features of a general class of higher-derivative theories of quantum gravity

Abstract

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.

Quantum corrected gravitational potential beyond monopole-monopole interactions

“…IV. Furthermore, we comment that, for the gravitational interaction of spin-0 particles, it is possible to generalize our results to arbitrary dimensions, as already discussed in the literature for modified theories of gravity in monopole-monopole sector (see [39,40] references therein). However, for spin-1 2 case and its spindependent contributions, this extension shall be a nontrivial task, since the definition of spin is particular to the dimension we are dealing with.…”

“…The observation at the end of the previous section trigger a question regarding the cancellation of Newtonian singularities. In particular, it would be interesting to investigate whether the regular behavior at r ¼ 0, observed in higherderivative models of gravity [4,40,51,52], persists after the inclusion of contributions beyond the static limit. This particular test is easily addressed in terms of the results presented in Sec.…”

“…II, however, it requires a slight modification in the way we interpret our framework. In the case of higher-derivative models, the form factor expansion appears at the level of the classical action [40,51,52], given by…”

Weak-field limit and regular solutions in polynomial higher-derivative gravities

“…The present work revisits two topics that have previously been investigated in the context of local and nonlocal higher-derivative gravity models, namely, the nonrelativistic limit [10,20,[44][45][46][47][48][49] and the collapse of small mass spherical shells [50,51]. Our focus is on general polynomial gravity, with a special attention given to the case of complex poles-Lee-Wick gravity-and also, for the sake of completeness, higher-order (degenerate) poles.…”

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

“…Finally, this might correspond to the condition of super-renormalizability [2,22]. At this point, it would be better to distinguish three types of renormalizable theory.…”