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 energy behaviour of the loop amplitudes. By power counting arguments, it is proved that the theory is super-renormalizable, i.e. only one-loop divergences survive. At classical level, black holes and cosmological solutions are singularity free.
The presence of an unstable massive spin-2 ghost state in the renormalizable theory of massive conformal gravity leads to a pair of complex poles appearing in the first sheet of the energy plane. Here we show that the positions of these poles are gauge dependent, which makes the theory unitary.
The Wilsonian renormalization group (RG) requires Euclidean signature. The conformal factor of the metric then has a wrong-sign kinetic term, which has a profound effect on its RG properties. In particular around the Gaussian fixed point, it supports a Hilbert space of renormalizable interactions involving arbitrarily high powers of the gravitational fluctuations. These interactions are characterised by being exponentially suppressed for large field amplitude, perturbative in Newton's constant but non-perturbative in Planck's constant. By taking a limit to the boundary of the Hilbert space, di…
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 shown that, at least in the cases of specific cosmological backgrounds, that the unphysical massive ghost which is present in the spectrum of such theories is not growing up as a physical excitation and remains in the vacuum state, until the initial frequency of the perturbation is close to the Planck order of magnitude. In this situation the existing versions …
We consider gravitational quasinormal modes of the static and spherically-symmetric dirty black holes in the effective theory of gravity which is renormalizable at the two-loop level. It is demonstrated that using the WKB-Padé summation proposed in \cite{jaOp} one can achieve sufficient accuracy to calculate corrections to the complex frequencies of the quasinormal modes caused by the Goroff-Sagnotti curvature terms. It is shown that the Goroff-Sagnotti correction (with our choice of the sign of the coupling constant) increases damping of the fundamental modes (except for the lowest fundamenta…
We discuss stability issues of Schwarzschild black hole in non-local gravity. It is shown that the stability analysis of black hole for the unitary and renormalizable non-local gravity with $γ_2=-2γ_0$ cannot be performed in the Lichnerowicz operator approach. On the other hand, for the unitary and non-renormalizable case with $γ_2=0$, the black hole is stable against the metric perturbations. For non-unitary and renormalizable local gravity with $γ_2=-2γ_0={\rm const}$ (fourth-order gravity), the small black holes are unstable against the metric perturbations. This implies that what makes the…
We develop a self-consistent $Spin(4,4)$-invariant model of the unification of gravity with weak $SU(2)$ gauge and Higgs fields in the visible and invisible sectors of our Universe. We consider a general case of the graviweak unification, including the higher-derivative super-renormalizable theory of gravity, which is a unitary, asymptotically-free and perturbatively consistent theory of the quantum gravity.
We analyze the R + R2 model of quantum gravity where terms quadratic in the curvature tensor are added to the General Relativity action. This model was recently proved to be a self-consistent quantum theory of gravitation, being both renormalizable and unitary. The model can be made practically indistinguishable from General Relativity at astrophysical and cosmological scales by the proper choice of parameters.
One of the main advantages of super-renormalizable higher derivative quantum gravity models is the possibility to derive exact beta functions, by making perturbative one-loop calculations. We perform such a calculation for the Newton constant by using the Barvinsky-Vilkovisky trace technology. The result is well-defined in a large class of models of gravity in the sense that the renormalization group beta functions do not depend on the gauge-fixing condition. Finally, we discuss the possibility to apply the results to a large class of nonlocal gravitational theories which are free of massive g…
Affine quantization is a parallel procedure to canonical quantization, which is ideally suited to deal with non-renormalizable scalar models as well as quantum gravity. The basic applications of this approach lead to the common goals of any quantization, such as Schroedinger's representation and Schroedinger's equation. Careful attention is paid toward seeking favored classical variables, which are those that should be promoted to the principal quantum operators. This effort leads toward classical variables that have a constant positive, zero, or negative curvature, which typically characteriz…
For any fundamental quantum field theory, unitarity, renormalizability, and relativistic invariance are considered to be essential properties. Unitarity is inevitably connected to the probabilistic interpretation of the quantum theory, while renormalizability guarantees its completeness. Relativistic invariance, in turn, is a symmetry which derives from the structure of spacetime. So far, the perturbative attempt to formulate a fundamental local quantum field theory of gravity based on the metric field seems to be in conflict with at least one of these properties. In quantum Hořava gravity, a …
We analyse scale invariant quadratic quantum gravity incorporating non-minimal coupling to a multiplet of scalar fields in a gauge theory, with particular emphasis on the consequences for its interpretation resulting from a transformation from the Jordan frame to the Einstein frame. The result is the natural emergence of a de Sitter space solution which, depending the gauge theory and region of parameter space chosen, can be free of ghosts and tachyons, and completely asymptotically free. In the case of an SO(10) model, we present a detailed account of the spontaneous symmetry breaking, and we…
We explicitly compute the tree-level on-shell four-graviton amplitudes in four, five and six dimensions for local and weakly nonlocal gravitational theories that are quadratic in both, the Ricci and scalar curvature with form factors of the d'Alembertian operator inserted between. More specifically we are interested in renormalizable, super-renormalizable or finite theories. The scattering amplitudes for these theories turn out to be the same as the ones of Einstein gravity regardless of the explicit form of the form factors. As a special case the four-graviton scattering amplitudes in Weyl co…
The Wilsonian renormalization group (RG) requires Euclidean signature. The conformal factor of the metric then has a wrong-sign kinetic term, which has a profound effect on its RG properties. Generically for the conformal sector, complete flows exist only in the reverse direction (i.e. from the infrared to the ultraviolet). The Gaussian fixed point supports infinite sequences of composite eigenoperators of increasing infrared relevancy (increasingly negative mass dimension), which are orthonormal and complete for bare interactions that are square integrable under the appropriate measure. These…
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 (QFT). The price to pay is a massive ghost, which is due to the higher derivatives that the terms quadratic in the curvature imply. In this paper the quadratic gravity scenario is reviewed including recent progress on the related stability problem of higher derivative theories. The renormalization of the theory is also reviewed and the final form of the full ren…
Newtonian potential from scattering amplitudes in super-renormalizable gravity
School of Physics and Electronic Engineering, Shanxi Normal University（山西师范大学物理与电子工程学院）；College of Physical Science and Technology, Hebei University（河北大学物理科学与技术学院）
Comment on "Arnowitt--Deser--Misner representation and Hamiltonian analysis of covariant renormalizable gravity" by M. Chaichian, M. Oksanen, A. Tureanu
本文对M. Chaichian，M. Oksanen，A. Tureanu（Eur. Phys. J. C 71，1657（2011））是不正确的;真正的约束代数与他们所声称的动量约束的选择不同。我们盲目接受他们的约束代数的正确性，导致我们得出结论，错误的是，作者提出的一些模型（共享相同的约束代数）在空间同构下不是不变的。我们用Noether第二定理“证明”了这一点（见论文的第一版），但是我们发现了计算中的一个错误。空间双同态的微分恒等式是完整的，因此它们的作用量是不变的;但在这种情况下，空间双同态的规范对称性不能与它们的代数相容。我们现在明确地证明，实际的代数约束是不同的，并简要地描述它如何影响发电机和规范变换的领域。
It is well-known that perturbative quantum gravity is non-renormalizable. The metric or vierbein has generally been used as the variable to quantize in perturbative quantum gravity. In this essay, we show that one can use the spin connection instead, in which case it is possible to obtain a ghost-free renormalizable theory of quantum gravity. Furthermore in this approach, gravitational analogs of particle physics phenomena can be studied. In particular, we study the gravitational Higgs mechanism using spin connection as a gauge field, and show that this provides a mechanism for the effective r…
We present 48 further examples, in addition to the 10 identified in [1], of ghost-and-tachyon-free critical cases of parity-conserving Poincaré gauge theories of gravity (PGT$^+$) that are also power-counting renormalizable (PCR). This is achieved by extending the range of critical cases considered. Of the new PCR theories, seven have 2 massless degrees of freedom (d.o.f.) in propagating modes and a massive $0^-$ or $2^-$ mode, eight have only 2 massless d.o.f., and 33 have only massive mode(s). We also clarify the treatment of nonpropagating modes in determining whether a theory is PCR.
We propose a class of multidimensional higher derivative theories of gravity without extra real degrees of freedom besides the graviton field. The propagator shows up the usual real graviton pole and extra complex conjugates poles that do not contribute to the absorptive part of the physical scattering amplitudes. Indeed, they may consistently be excluded from the asymptotic observable states of the theory making use of the Lee-Wick and Cutkoski, Landshoff, Olive and Polkinghorne prescription for the construction of a unitary S-matrix. Therefore, the spectrum consists on the graviton and short…
It is well known that General Relativity cannot be considered under the standard of a perturbatively renormalizable quantum field theory, but asymptotic safety is taken into account as a possibility for the formulation of gravity as a non-perturbative renormalizable theory. Recently, the entropy argument has however stepped into the discussion claiming for a "no-go" to the asymptotic safety argument. In this paper, we present simple counter-examples, considering alternative theories of gravity, to the entropy argument as further indications, among others, on the possible flows in the assumptio…
It has been argued that Horava gravity needs to be extended to include terms that mix spatial and time derivatives in order avoid unacceptable violations of Lorentz invariance in the matter sector. In an earlier paper we have shown that including such mixed derivative terms generically leads to 4th instead of 6th order dispersion relations and this could be (naively) interpreted as a threat to renormalizability. We have also argued that power-counting renormalizability is not actually compromised, but instead the simplest power-counting renormalizable model is not unitary. In this paper we con…
