We consider the asymptotic-safety scenario for quantum gravity which constructs a non-perturbatively renormalisable quantum gravity theory with the help of the functional renormalisation group. We verify the existence of a non-Gaussian fixed point and include a running curvature-ghost coupling as a first step towards the flow of the ghost sector of the theory. We find that the scalar curvature-ghost coupling is asymptotically free and RG relevant in the ultraviolet. Most importantly, the property of asymptotic safety discovered so far within the Einstein-Hilbert truncation and beyond remains stable under the inclusion of the ghost flow.
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…
A class of dynamical dark energy models is constructed through an extended version of fermion fields corresponding to phantom dark ghost spinors, which are spin one half with mass dimension one. We find that if these spinors interact with torsion fields in a homogeneous and isotropic universe, then it does not imply any future dark energy singularity or any abrupt event, though the fermion has a negative kinetic energy. In fact, the equation of state of this dark energy model will asymptotically approach the value $w=-1$ from above without crossing the phantom divide and inducing therefore a d…
In full Horndeski theories, we show that the static and spherically symmetric black hole (BH) solutions with a static scalar field~$ϕ$ whose kinetic term~$X$ is nonvanishing on the BH horizon are generically prone to ghost/Laplacian instabilities. We then search for asymptotically Minkowski hairy BH solutions with a vanishing $X$ on the horizon free from ghost/Laplacian instabilities. We show that models with regular coupling functions of $ϕ$ and $X$ result in no-hair Schwarzschild BHs in general. On the other hand, the presence of a coupling between the scalar field and the Gauss-Bonnet (GB) …
If the kinetic interactions of a Lorentz-invariant massive graviton are Einstein-Hilbert, then the only possible potential terms free from the Boulware-Deser ghost are those of de Rham, Gabadadze and Tolley (dRGT). We point out there are other possibilities if the kinetic terms are not required to be Einstein-Hilbert. We construct pseudo-linear ghost-free potentials, terms that derive in a natural way from the linear theory. The simplicity of this approach allows us to construct diffeomorphism non-invariant higher-derivative interaction terms that do not introduce ghosts. We conjecture that th…
We construct exact pp-wave solutions of ghost-free infinite derivative gravity and demonstrate that the sourceless theory does not bring any pp-wave solutions save for that of Einstein's gravity. These waves described in the Kerr-Schild form also solve the linearized field equations of the theory. We also find an exact gravitational shock wave with non-singular curvature invariants and with a finite limit in the ultraviolet regime of non-locality which is in contrast to the divergent limit in Einstein's theory.
The detailed calculations of the energy in the ghost-free massive gravity theory is presented. The energy is defined in the standard way within the canonical approach, but to evaluate it requires resolving the Hamiltonian constraints, which are known, in general, only implicitly. Fortunately, the constraints can be explicitly obtained and resolved in the spherically symmetric sector, which allows one to evaluate the energy. It turns out that the energy is positive for globally regular and asymptotically flat fields constituting the "physical sector" of the theory. In other cases the energy can…
The energy in the ghost-free massive gravity theory is calculated via explicitly resolving the initial value constraints for spherically symmetric deformations of flat space. It turns out that the energy is positive in some cases, but in other cases it can be negative and even unbounded from below. This could suggest that ghost instability is present. However, it seems that the negative energy states cannot communicate with the positive energy sector since the corresponding solutions of the constraint equations are either not globally defined, not asymptotically flat, or singular. As a result,…
Ghosts versus Unstable Particles in Quantum Field Theory
Departamento de Física de Partículas, Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学加利西亚高能物理研究所粒子物理系）
Form factors constitute the key building block when organising the gravitational dynamics in terms of a curvature expansion. They generalise the concept of momentum-dependent couplings to curved spacetime. Moreover, they may capture modifications of the gravitational interactions at high energy scales in a non-perturbative way. We briefly review the role of form factors in various quantum gravity programmes with special emphasis on non-local, ghost-free gravity and asymptotically safe gravity. In this context, we introduce a quantum gravity motivated scalar toy model, which demonstrates that L…
We present the construction of a gravitational action including an infinite series of higher derivative terms. The outcome is a classically consistent completion of a well-studied quadratic curvature theory. The closed form for the full action is ghost-free bimetric theory, describing the interactions of a massive and a massless spin-2 field. At energies much smaller than the spin-2 mass scale, the theory reduces to general relativity. For energies comparable to the spin-2 mass, the higher derivative terms completing the Einstein-Hilbert action capture the effects of the additional massive spi…
We consider the Hassan-Rosen bimetric field equations in vacuum when the two metrics share a single common null direction in a spherically symmetric configuration. By solving these equations, we obtain a class of exact solutions of the generalized Vaidya type parametrized by an arbitrary function. Besides not being asymptotically flat, the found solutions are nonstationary admitting only three global spacelike Killing vector fields which are the generators of spatial rotations. Hence, these are spherically symmetric bimetric vacuum solutions with the minimal number of isometries. The absence o…
In this paper, we demonstrate that the Wald's entropy for any spherically symmetric blackhole within an infinite derivative theory of gravity is determined solely by the area law. Thus, the infrared behaviour of gravity is captured by the Einstein-Hilbert term, provided that the massless graviton remains the only propagating degree of freedom in the spacetime.
We investigate the thermodynamics of spherically symmetric black hole solutions in a four-dimensional Einstein--Yang-Mills-SU(2) theory with a negative cosmological constant. Special attention is paid to configurations with a unit magnetic charge. We find that a set of Reissner-Nordström--Anti-de Sitter black holes can become unstable to forming non-Abelian hair. However, the hairy black holes are never thermodynamically favoured over the full set of abelian monopole solutions. The thermodynamics of the generic configurations possessing a noninteger magnetic charge is also discussed.
We consider the problem for the classification of static and asymptotically flat Einstein-Maxwell-dilaton spacetimes with a photon sphere. It is first proven that the photon spheres in Einstein-Maxwell-dilaton gravity have constant mean and constant scalar curvature. Then we derive some relations between the mean curvature and the physical characteristics of the photon spheres. Using further the symmetries of the dimensionally reduced Einstein-Maxwell-dilaton field equations we show that the lapse function, the electrostatic potential and the dilaton field are functionally dependent in the pre…
In this paper, we are interested in a model of exact asymptotically flat charged hairy black holes in the background of dilaton potential. We study the weak gravitational lensing in the spacetime of hairy black hole in Einstein-Maxwell theory with a non-minimally coupled dilaton and its non-trivial potential. In doing so, we use the optical geometry of the flat charged hairy black hole for some range of parameter $γ$. For this purpose, by using Gauss-Bonnet theorem, we obtain the deflection angle of photon in a spherically symmetric and asymptotically flat spacetime. Moreover, we also investig…
Three-dimensional Einstein-Maxwell theory with non trivial asymptotics at null infinity is solved. The symmetry algebra is a Virasoro-Kac-Moody type algebra that extends the bms3 algebra of the purely gravitational case. Solution space involves logarithms and provides a tractable example of a polyhomogeneous solution space. The associated surface charges are non-integrable and non-conserved due to the presence of electromagnetic news. As in the four dimensional purely gravitational case, their algebra involves a field-dependent central charge.
In this work we shall address the ghost issue of $F\left( R,\mathcal{G} \right)$ gravity, which is known to be plagued with ghost degrees of freedom. These ghosts occur due to the presence of higher than two derivatives in the field equations, and can arise even when considering cosmological perturbations, where superluminal modes may arise in the theory. If we consider the quantum theory, the ghosts generate the negative norm states, which give the negative probabilities, and therefore the ghosts are physically inconsistent. Motivated by the importance of $F\left( R,\mathcal{G} \right)$ gravi…
In this paper we will study the complete equations of motion for a ghost free quadratic curvature infinite derivative gravity. We will argue that within the scale of non-locality, Schwarzschild-type singular metric solution is not {\it permissible}. Therefore, Schwarzschild-type vacuum solution which is a prediction in Einstein-Hilbert gravity may {\it not} persist within the region of non-locality. We will also show that just quadratic curvature gravity, without infinite derivatives, always allows Schwarzschild-type singular metric solution.
More than three decades ago quadratic gravity was found to present a perturbative, renormalizable and asymptotically free theory of quantum gravity. Unfortunately the theory appeared to have problems with a spin-2 ghost. In this essay we revisit quadratic gravity in a different light by considering the case that the asymptotically free interaction flows to a strongly interacting regime. This occurs when the coefficient of the Einstein-Hilbert term is smaller than the scale $Λ_{\mathrm{QG}}$ where the quadratic couplings grow strong. Here QCD provides some useful insights. By pushing the analog…
We show that there can be no new Lorentz invariant kinetic interactions free from the Boulware-Deser ghost in four dimensions in the metric formulation of gravity, beyond the standard Einstein-Hilbert, up to total derivatives. We use dimensional deconstruction as a way to motivate a non-linear ansatz for potential new ghost free kinetic interactions for massive gravity, bi-gravity and multi-gravity in four and higher dimensions. These interactions descend from Lovelock terms, and so naively one might expect the interactions to be ghost free. However we show that these new interactions inevitab…
In this paper, we study Einstein gravity extended with Ricci polynomials and derive the constraints on the coupling constants from the considerations of being ghost free, exhibiting an $a$-theorem and maintaining causality. The salient feature is that Einstein metrics with appropriate effective cosmological constants continue to be solutions with the inclusion of such Ricci polynomials and the causality constraint is automatically satisfied. The ghost free and $a$-theorem conditions can only be both met starting at the quartic order. We also study these constraints on general Riemann cubic gra…
