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It is shown that polynomial gravity theories with more than four derivatives in each scalar and tensor sectors have a regular weak-field limit, without curvature singularities. This is achieved by proving that in these models the effect of…
The inclusion of higher derivatives is a necessary condition for a renormalizable or superrenormalizable local theory of quantum gravity. On the other hand, higher derivatives lead to classical instabilities and a loss of unitarity at the…
We suggest and briefly review a new sort of superrenormalizable models of higher derivative quantum gravity. The higher derivative terms in the action can be introduced in such a way that all the unphysical massive states have complex…
Perturbation theory for gravity in dimensions greater than two requires higher derivatives in the free action. Higher derivatives seem to lead to ghosts, states with negative norm. We consider a fourth order scalar field theory and show…
Understanding the role of higher derivatives is probably one of the most relevant questions in quantum gravity theory. Already at the semiclassical level, when gravity is a classical background for quantum matter fields, the action of…
One of the remarkable differences between renormalizable quantum gravity with four-derivative action and its superrenormalizable polynomial generalizations is that the latter admit a more sophisticated particle mass spectrum. Already in the…
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…
We review a class of higher derivative theories of gravity consistent at quantum level. This class is marked by a non-polynomal entire function (form factor), which averts extra degrees of freedom (including ghosts) and improves the high…
We consider the problem of Newtonian singularity in the wide class of higher derivative gravity models, including the ones which are renormalizable and super-renormalizable at the quantum level. The simplest version of the singularity-free…
We review some of the recent results which can be useful for better understanding of the problem of stability of vacuum and in general classical solutions in higher derivative quantum gravity. The fourth derivative terms in the purely…
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantisation. We find that a 4-derivative degree of…
Generic massive gravity models in the unitary gauge correspond to a self-gravitating medium with six degrees of freedom. It is widely believed that massive gravity models with six degrees of freedom have an unavoidable ghost-like…
In this paper we study perturbatively an extension of the Stelle higher derivative gravity involving an infinite number of derivative terms. We know that the usual quadratic action is renormalizable but is not unitary because of the…
A scalar field theory with 4-derivative kinetic terms and 4-derivative cubic and quartic couplings is presented as a proxy for quantum quadratic gravity (QQG). The scalar theory is renormalizable and asymptotically free and the remaining…
We hereby introduce and extensively study a class of non-polynomial higher derivative theories of gravity that realize a ultraviolet (UV) completion of Einstein general relativity. These theories are unitary (ghost free) and at most only…
Adding terms quadratic in the curvature to the Einstein-Hilbert action renders gravity renormalizable. This property is preserved in the presence of the most general renormalizable couplings with (and of) a generic quantum field theory…
We introduce new techniques that can preserve unitarity of the system including ghost particles. Negative norms of the particles can be involved in zero-norm states by constraints of the physical space. These are useful to apply the…
In this work we study a modified theory of gravity that contains up to fourth order spatial derivatives as a model for the Horava-Lifshitz gravity. The propagator is evaluated and, as a result, it is obtained one extra pole corresponding to…
In this paper we study perturbatively an extension of the Stelle higher derivative gravity involving an infinite number of derivative terms. We know that the usual quadratic action is renormalizable but suffers of the unitarity problem…
We explore how the stability of metric perturbations in higher derivative theories of gravity depends on the energy scale of initial seeds of such perturbations and on a typical energy scale of the gravitational vacuum background. It is…