Einstein gravity as spontaneously broken Weyl gravity

We study the locally conformal invariant Weyl theory of gravitation and introduce a conformally coupled scalar field. Einstein gravity is induced by spontaneous breaking of the local conformal symmetry in an effective long range approximation. The effective potential for the scalar field is calculated at the one-loop level up to curvature squared in order in an arbitrary curved background. The non-zero vacuum expectation value of the scalar field induces the dimensional Einstein's gravitational coupling constant stably in case ofR > 0. ForR < 0, the phase transition occurs from the symmetric phase to the broken phase as the curvature decreases. This theory may be an attractive candidate for the primordial inflationary universe scenario.     

Impact of topology in foliated quantum Einstein gravity

We use a functional renormalization group equation tailored to the Arnowitt–Deser–Misner formulation of gravity to study the scale dependence of Newton’s coupling and the cosmological constant on a background spacetime with topology \(S^1 \times S^d\). The resulting beta functions possess a non-trivial renormalization group fixed point, which may provide the high-energy completion of the theory through the asymptotic safety mechanism. The fixed point is robust with respect to changing the parametrization of the metric fluctuations and regulator scheme. The phase diagrams show that this fixed point is connected to a classical regime through a crossover. In addition the flow may exhibit a regime of “gravitational instability”, modifying the theory in the deep infrared. Our work complements earlier studies of the gravitational renormalization group flow on a background topology \(S^1 \times T^d\) (Biemans et al. Phys Rev D 95:086013, 2017, Biemans et al. arXiv:1702.06539, 2017) and establishes that the flow is essentially independent of the background topology.     

Bimetric renormalization group flows in quantum Einstein gravity

The formulation of an exact functional renormalization group equation for quantum Einstein gravity necessitates that the underlying effective average action depends on two metrics, a dynamical metric giving the vacuum expectation value of the quantum field, and a background metric supplying the coarse graining scale. The central requirement of “background independence” is met by leaving the background metric completely arbitrary. This bimetric structure entails that the effective average action may contain three classes of interactions: those built from the dynamical metric only, terms which are purely background, and those involving a mixture of both metrics. This work initiates the first study of the full-fledged gravitational RG flow, which explicitly accounts for this bimetric structure, by considering an ansatz for the effective average action which includes all three classes of interactions. It is shown that the non-trivial gravitational RG fixed point central to the asymptotic safety program persists upon disentangling the dynamical and background terms. Moreover, upon including the mixed terms, a second non-trivial fixed point emerges, which may control the theory’s IR behavior.     

Irreducibility of the Weyl algebra in loop quantum gravity

The irreducibility of the standard Weyl algebra representation in loop quantum gravity is proven using a very short and direct argument.     

Bimetric truncations for quantum Einstein gravity and asymptotic safety

In the average action approach to the quantization of gravity the fundamental requirement of “background independence” is met by actually introducing a background metric but leaving it completely arbitrary. The associated Wilsonian renormalization group defines a coarse graining flow on a theory space of functionals which, besides the dynamical metric, depend explicitly on the background metric. All solutions to the truncated flow equations known to date have a trivial background field dependence only, namely via the classical gauge fixing term. In this paper, we analyze a number of conceptual issues related to the bimetric character of the gravitational average action and explore a first nontrivial bimetric truncation in the simplified setting of conformally reduced gravity. Possible implications for the Asymptotic Safety program and the cosmological constant problem are discussed in detail.     

Einstein equations and Fierz-Pauli equations with self-interaction in quantum gravity

The Einstein equations can be written as Fierz-Pauli equations with self-interaction, together with the covariant Hilbert-gauge condition, where W denotes the covariant wave operator and G _ik the Einstein tensor of the metric g _ik collecting all nonlinear terms of Einstein's equations. As is known, there do not, however, exist plane-wave solutions _ik(z)with g ^ik Z,_i Z,_k=0of these equations such that what is essential to the introduction of gravitons is not satisfied in general relativity. This nonexistence corresponds with the uncertainty relation,p(g*)²(x)³h hG/ c ³ concerning the total nonlinear gravitational field g ^*ik =g ^k + ^k .     

Non-universal shear viscosity from Einstein gravity

A very famous result of gauge/gravity duality is the universality of the ratio of shear viscosity to entropy density in every field theory holographically dual to classical, two-derivative (Einstein) gravity. We present a way to obtain deviation from this universality by breaking the rotational symmetry spontaneously. In anisotropic fluids additional shear modes exist and their corresponding shear viscosities may be non-universal. We confirm this by explicitly calculating the shear viscosities in a transversely isotropic background, a p-wave superfluid, and study its critical behavior. This is a first decisive step towards further applications of gauge/gravity duality to physical systems.     

Inflation from quantum gravity

A model for inflation based on a quantum gravity scenario is presented. The process allows inflation of a Planck size bubble to the observed universe.     

Conformal invariance in Weyl gravity

A conformal-invariant model of Weyl gravity, based on a nondecomposable representation of the conformal group, allows one to have a conformal-invariant propagator in an arbitrary gauge, as well as a conformal-invariant gauge-fixing term in the Lagrangian approach. It is shown that in the gauge-invariant sector this theory coincides with ordinary Weyl gravity (with conformal-noninvariant gauge fixing). The corresponding BRST transformations are found and are used for derivation of the Slavnov-Taylor identities.     

2D quantum gravity from quantum entanglement

In quantum systems with many degrees of freedom the replica method is a useful tool to study the entanglement of arbitrary spatial regions. We apply it in a way that allows them to backreact. As a consequence, they become dynamical subsystems whose position, form, and extension are determined by their interaction with the whole system. We analyze, in particular, quantum spin chains described at criticality by a conformal field theory. Its coupling to the Gibbs' ensemble of all possible subsystems is relevant and drives the system into a new fixed point which is argued to be that of the 2D quantum gravity coupled to this system. Numerical experiments on the critical Ising model show that the new critical exponents agree with those predicted by the formula of Knizhnik, Polyakov, and Zamolodchikov.     

Cosmological solution of the Einstein—Weyl equation

The accurate integration of the Einstein—Weyl field equations is considered for the case when the spinor field depends only on the time, while the metric specifies a uniform space—time of type I in the Bianci classification, i.e., a particular case of a Steckel space of type (3.0). Tomsk State Pedagogical University. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 69–78, November, 1998.     

Unexpected spin-off from quantum gravity

We propose a novel way of investigating the universal properties of spin systems by coupling them to an ensemble of causal dynamically triangulated lattices, instead of studying them on a fixed regular or random lattice. Somewhat surprisingly, graph-counting methods to extract high- or low-temperature series expansions can be adapted to this case. For the two-dimensional Ising model, we present evidence that this ameliorates the singularity structure of thermodynamic functions in the complex plane, and improves the convergence of the power series.     

Half-integral spin from quantum gravity

For a certain class of three-manifolds, the angular momentum of an asymptotically flat quantum gravitational field can have half-integral values. In the absence of a full theory of quantum gravity, this result relies on a set of apparently natural assumptions governing the kinematics of such a theory. A key feature is that state vectors are in general invariant only under asymptotically trivial diffeomorphisms that can be continuously deformed to the identity. Angular momentum is associated with diffeomorphisms that look asymptotically like rotations; and the question of whether half-integral values occur depends on whether the diffeomorphism associated with a 2 rotation is itself deformable to the identity.This essay received the fourth award from the Gravity Research Foundation for the year 1981-Ed.     

The Einstein action of Riemannian metrics and its relation to quantum gravity and thermodynamics

The Einstein action evaluated on Riemannian metrics is investigated. It is neither bounded below or above and its critical points are saddle points. This probably means that the functional integral will not converge, and is related to the negative specific heat of self gravitating systems and the breakdown of the validity of the canonical ensemble. The contribution from Wheeler's foam-like structures is shown to have the correct sign for convergence and to contribute positively to the free energy.     

Graviton propagator from background-independent quantum gravity

We study the graviton propagator in Euclidean loop quantum gravity. We use spin foam, boundary-amplitude, and group-field-theory techniques. We compute a component of the propagator to first order, under some approximations, obtaining the correct large-distance behavior. This indicates a way for deriving conventional spacetime quantities from a background-independent theory.     

New holographic Weyl superconductors in Lifshitz gravity

We build holographic p-wave conductor(insulator)/superconductor models via the numerical method with a new form of Weyl coupling in five-dimensional Lifshitz gravity, and then investigate how the Weyl coupling parameter γ and the Lifshitz scaling parameter z affect the superconductor models.In the conductor/superconductor model, an increase in the Weyl correction(Lifshitz scaling)enhances(inhibits) the superconductor phase transition. Meanwhile, both the Weyl correction(when the Lifshitz parameter is large enough and fixed) and the Lifshitz scaling suppress the growth of the real part of the conductivity. The Weyl correction used here(CB~2) shows weaker effects on the critical value than the previous Weyl correction(CF~2). In the insulator/superconductor model, larger vaules of the Weyl parameter hinder the formation of condensate. However, in increase in the Lifshitz scaling enhances the appearance of condensate. In addition, the calculation suggests that a competitive relation may exist between the Weyl correction and the Lifshitz scaling.     

Bianchi and Weyl equations as sufficient equations for Einstein spaces

When the Bianchi equation and the wave equation for the Weyl spinor are written in the form which they take for Einstein spaces, but with the symmetric 4-spinor _ABCD considered arbitrary and with the background space unspecified, ^EA _EBCD=0; (+12) _ABCD –6(AB ^EF ( _CD )EF =0 it is shown that — in general — for this pair of equations to be consistent, the background space has to be an Einstein space, and the symmetric 4-spinor _ABCD has to be the Weyl spinor of this space.