We explore a background-independent theory of composite gravity. The vacuum expectation value of the composite metric satisfies Einstein's equations (with corrections) as a consistency condition, and selects the vacuum spacetime. A gravitational interaction then emerges in vacuum correlation functions. The action remains diffeomorphism invariant even as perturbation theory is organized about the dynamically selected vacuum spacetime. We discuss the role of nondynamical clock and rod fields in the analysis, the identification of physical observables, and the generalization to other theories including the standard model.
We investigate the coupling between a Galileon scalar field and massive gravity through composite metrics. We derive the full set of equations of motion for a flat Friedmann-Robertson-Walker background, and study linear perturbations around it. Generally, the nonminimal coupling with the composite metric will excite all 6 degrees of freedom of the spatial metric perturbations, one of which may correspond to the Boulware-Deser ghost.
We study a 7-dimensional brane world scenario with a Ricci-flat 3-brane residing in the core of a composite monopole defect, i.e. a defect composed of a 'tHooft-Polyakov and a global monopole. Admitting a direct interaction between the two bosonic sectors of the theory, we analyse the structure of the space-time in the limits of small, respectively large direct interaction coupling constant. For large direct interaction, the global monopole disappears from the system and leaves behind a negative cosmological constant in the bulk such that gravity-localising solutions are possible without the a…
We present a metric-independent, diffeomorphism-invariant model with interacting fermions that contains a massless composite graviton in its spectrum. The model is motivated by the supersymmetric D-brane action, modulated by a fermion potential. The gravitational coupling is related to new physics at the cutoff scale that regularizes UV divergences. We also speculate on possible extensions of the model.
We study the role of composite operators in the Asymptotic Safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources we are able to keep track of operators which do not belong to the exact theory space and/or are normally discarded in a truncation. Typical examples are geometric operators such as volumes, lengths, or geodesic distances. We show that this set-up allows to investigate the scaling properties of various interesting operators via a suitable exact renormalization group equation. We test our framework in several settings, i…
This paper is dedicated to scrutinizing the cosmology in massive gravity. A matter field of the dark sector is coupled to an effective composite metric while a standard matter field couples to the dynamical metric in the usual way. For this purpose, we study the dynamical system of cosmological solutions by using phase analysis, which provides an overview of the class of cosmological solutions in this setup. This also permits us to study the critical points of the cosmological equations together with their stability. We show the presence of stable attractor de Sitter critical points relevant t…
We explore scenarios in which the graviton is not a fundamental degree of freedom at short distances but merely emerges as an effective degree of freedom at long distances. In general, the scale of such graviton `compositeness', Lambda_g, can only be probed by measuring gravitational forces at short distances, which becomes increasingly difficult and eventually impossible as the distance is reduced. Here, however, we point out that if supersymmetry is an underlying symmetry, the gravitino can be used as an alternative probe to place a limit on Lambda_g in a collider environment, by demonstrati…
We present a first analysis of a nonperturbative approach to quantum gravity based on a representation of quantum field theory in terms of stochastic processes. The stochastic description accommodates a physical Lorentz-invariant ultraviolet regulator that provides a novel description of physics at ultra-short distances. In a stochastic composite gravity model we demonstrate the evolution of a generic initial field configuration towards an equilibrium in which the composite spacetime metric fluctuates about a flat spacetime. We argue that fluctuations about the vacuum give rise to an emergent …
We consider a theory of scalars minimally coupled to an auxiliary background metric. The theory is generally covariant and subject to the constraint of vanishing energy-momentum tensor. Eliminating the auxiliary metric leads to a reparametrization invariant, non-polynomial, metric-independent action for the scalar fields. Working in the limit of a large number of physical scalars, a composite massless spin-2 state, the graviton, was identified in previous work, in a two-into-two scalar scattering process. Here, we further explore the possibility that dynamical emergent gravity is a natural fea…
Emergence of dynamical tensor fields in composite models of gravity
Center for Theoretical Physics and College of Physics, Jilin University（吉林大学理论物理中心及物理学院）；Department of Physics and Astronomy, Kwansei Gakuin University（关西学院大学物理与天文学系）
In the context of massive gravity, bi-gravity and multi-gravity non-minimal matter couplings via a specific composite effective metric were investigated recently. Even if these couplings generically reintroduce the Boulware-Deser ghost, this composite metric is unique in the sense that the ghost reemerges only beyond the decoupling limit and the matter quantum loop corrections do not detune the potential interactions. We consider non-minimal {\it derivative} couplings of the composite metric to matter fields for a specific subclass of Horndeski scalar-tensor interactions. We first explore thes…
Whenever an alternative theory of gravity is formulated in a background Minkowski space, the conditions characterizing admissible coordinate systems, in which the alternative theory of gravity may be applied, play an important role. We here propose Lorentz covariant coordinate conditions for the composite theory of pure gravity developed from the Yang-Mills theory based on the Lorentz group, thereby completing this previously proposed higher derivative theory of gravity. The physically relevant static isotropic solutions are determined by various methods, the high-precision predictions of gene…
Models of quantum gravity imply a fundamental revision of our description of position and momentum that manifests in modifications of the canonical commutation relations. Experimental tests of such modifications remain an outstanding challenge. These corrections scale with the mass of test particles, which motivates experiments using macroscopic composite particles. Here we consider a challenge to such tests, namely that quantum gravity corrections of canonical commutation relations are expected to be suppressed with increasing number of constituent particles. Since the precise scaling of this…
Non-Abelian gauge theories with composite fields are examined in the background field method. Generating functionals of Green's functions for a Yang--Mills theory with composite and background fields are introduced, including the generating functional of vertex Green's functions (effective action). The corresponding Ward identities are obtained, and the issue of gauge dependence is investigated. A gauge variation of the effective action is found in terms of a nilpotent operator depending on the composite and background fields. On-shell independence from the choice of gauge fixing for the effec…
It was recently observed in \cite{Park:2014tia} that the holographic nature of gravity may hold a key to quantization of gravity. The so-called "holographic quantization" has been carried out in \cite{Park:2014noa,Park:2015ota} for Einstein gravity in a flat background. Generalizing the procedure to a curved background is the main goal of the present work. In particular, we consider the Einstein action expanded around a Schwarzschild background
Massive gravity in the presence of doubly coupled matter field via en effective composite metric yields an accelerated expansion of the universe. It has been recently shown that the model admits stable de Sitter attractor solutions and could be used as a dark energy model. In this work, we perform a first analysis of the constraints imposed by the SNIa, BAO and CMB data on the massive gravity model with the effective composite metric and show that all the background observations are mutually compatible at the one sigma level with the model.
It is generally believed that a full-fledged theory of quantum gravity should exhibit background independence and diffeomorphism invariance. In its most general form, the latter comprises field redefinitions, which are diffeomorphisms in configuration space. We show that any path-integral approach to quantum gravity leads to a tension between these properties, such that they cannot hold simultaneously.
A gauge theory of gravity based on a nonlinear realization (NLR) of the local Conform-Affine (CA) group of symmetry transformations is presented. The coframe fields and gauge connections of the theory are obtained. The tetrads and Lorentz group metric are used to induce a spacetime metric. The inhomogenously transforming (under the Lorentz group) connection coefficients serve as gravitational gauge potentials used to define covariant derivatives accommodating minimal coupling of matter and gauge fields. On the other hand, the tensor valued connection forms serve as auxillary dynamical fields a…
It has been shown that the spectrum of quantum gravity contains at least two new modes in addition to the massless graviton: a massive spin-0 and a massive spin-2. We calculate their power spectrum during inflation and we argue that they could leave an imprint in the cosmic microwave background should their masses be below the inflationary scale.
I review the definition of n-point functions in loop quantum gravity, discussing what has been done and what are the main open issues. Particular attention is dedicated to gauge aspects and renormalization.
We deduce, in a general background gauge, the counter-term Lagrangian for pure quantum gravity to one-loop order. As an application, we evaluate the leading quantum correction to the classical gravitational potential, generated by the vacuum polarization. We find that, in specific background gauges, this yields the complete result for the one-loop quantum corrections to the Newtonian potential. This approach is also applied to calculate the $\ln(T)$ contributions in quantum gravity at high-temperature.
Background independence is often emphasized as an important property of a quantum theory of gravity that takes seriously the geometrical nature of general relativity. In a background-independent formulation, quantum gravity should determine not only the dynamics of space-time but also its geometry, which may have equally important implications for claims of potential physical observations. One of the leading candidates for background-independent quantum gravity is loop quantum gravity. By combining and interpreting several recent results, it is shown here how the canonical nature of this theor…
We examine the conditions under which the thermodynamic behaviour of gravity can be explained within an emergent gravity scenario, where the metric is defined as a composite operator. We show that due to the availability of a boundary of a boundary principle for the quantum effective action, Clausius-like relations can always be constructed. Hence, any true explanation of the thermodynamic nature of the metric tensor has to be referred to an equilibration process, associated to the presence of an H-theorem, possibly driven by decoherence induced by the pregeometric degrees of freedom, and thei…
We study the background scale independence in single-metric approximation to the functional renormalization group equation (FRGE) for quantum gravity and show that it is possible to formulate it without using higher-derivative gauge fixing in arbitrary dimensions if we adopt the Landau gauge and suitable cutoff scheme. We discuss this problem for both the linear and exponential splits of the metric into background and fluctuations. The obtained modified Ward identity for the global rescalings of the background metric can be combined with the FRGE to give a manifestly scale-invariant solution. …
The application of quantum theory to gravity is beset with many technical and conceptual problems. After a short tour d'horizon of recent attempts to master those problems by the introduction of new approaches, we show that the aim, a background independent quantum theory of gravity, can be reached in a particular area, 2d dilaton quantum gravity, without any assumptions beyond standard quantum field theory.
We investigate the problems of ghosts and stability in the framework of asymptotical safe theory of gravity in the Minkowski background. Within one loop corrections, we obtain explicitly the constraints on the coupling parameters. Applying them to the coupling constant recently-obtained at the fixed point, we find that the corresponding theory is both ghost-free and stable. Our results can be easily generalized to high order corrections.
A theorem of differential geometry is employed to locally embed a wide class of superstring backgrounds that admit a covariantly constant null Killing vector field in eleven-dimensional, Ricci-flat spaces. Included in this class are exact type IIB superstring backgrounds with non-trivial Ramond-Ramond fields and a class of supersymmetric string waves. The embedding spaces represent exact solutions to eleven-dimensional, vacuum Einstein gravity. A solution of eleven-dimensional supergravity is also embedded in a twelve--dimensional, Ricci-flat space.
Boosted and rotated tetrad backgrounds for the Minkowski space are studied in $f(T)$ gravity. We perform Lorentzian perturbations at first order around non-trivial backgrounds and show that some Lorentz modes can exhibit non-trivial dynamics and can propagate in time. This remarkable feature gives evidence of additional mode(s) in the Lorentzian sector which have no precedent in Lorentz-violating modified gravities, however they can cast doubts onto even theoretical viability of these models.
Gravitational effective field theories with nondynamical backgrounds explicitly break diffeomorphism and local Lorentz invariance. At the same time, to maintain observer independence the action describing these theories is required to be mathematically invariant under general coordinate transformations and changes of local Lorentz bases. These opposing effects of having broken spacetime symmetries but invariance under mathematical observer transformations can result in theoretical inconsistency unless certain conditions hold. The consistency constraints that must hold originate from Noether id…
We construct background-independent Noether charges in Topologically Massive Gravity with negative cosmological constant using its first-order formulation. The procedure is carried out by keeping track of the surface terms in the variation of the action, regardless the value of the gravitational Chern-Simons coupling $μ$. In particular, this method provides a definition of conserved quantities for solutions at the chiral point $μl = 1$ ($l$ is the AdS radius) that contain logarithmic terms (Log Gravity). It is also shown that the charge formula gives a finite result for warped AdS black holes …
We discuss various basic conceptual issues related to coarse graining flows in quantum gravity. In particular the requirement of background independence is shown to lead to renormalization group (RG) flows which are significantly different from their analogs on a rigid background spacetime. The importance of these findings for the asymptotic safety approach to Quantum Einstein Gravity (QEG) is demonstrated in a simplified setting where only the conformal factor is quantized. We identify background independence as a (the ?) key prerequisite for the existence of a non-Gaussian RG fixed point and…
Quantum gravity that describes the world beyond the Planck scale should be formulated in a background-metric independent manner. Such a background-free nature can be represented as a gauge equivalency under conformal transformations, called the BRST conformal symmetry. In this review, we present quantum field theories of gravity with such symmetry. Since we can choose any background owing to this symmetry as far as it is conformally flat, we here employ the cylindrical background. First, we briefly review the famous BRST Liouville-Virasoro algebra in 2D quantum gravity on $R \times S^1$. We th…
We invesigate analytically both the intermediate and late-time behaviour of the massive scalar field in the background of static spherically symmetric black hole solution in dilaton gravity with arbitrary coupling constant. The intermediate asymptotic behaviour of scalar field depends on the field's parameter mass as well as the multiple number l. On its turn, the late-time behaviour has the power law decay rate independent on coupling constant in the theory under consideration.
We consider the primordial gravity wave background produced by inflation. We compute the small anisotropy produced by the primordial scalar fluctuations.
The natural constraints for the weak-field approximation to composite gravity, which is obtained by expressing the gauge vector fields of the Yang-Mills theory based on the Lorentz group in terms of tetrad variables and their derivatives, are analyzed in detail within a canonical Hamiltonian approach. Although this higher derivative theory involves a large number of fields, only few degrees of freedom are left, which are recognized as selected stable solutions of the underlying Yang-Mills theory. The constraint structure suggests a consistent double coupling of matter to both Yang-Mills and te…
Field theories that are generally covariant but nongravitational at tree level typically give rise to an emergent gravitational interaction whose strength depends on a physical regulator. We consider emergent gravity models in which scalar fields assume the role of clock and rulers, addressing the problem of time in quantum gravity. We discuss the possibility of nontrivial dynamics for clock and ruler fields, and describe some of the consequences of those dynamics for the emergent gravitational theory.
We investigate generally covariant theories which admit a Fierz-Pauli mass term for metric perturbations around an arbitrary curved background. For this we restore the general covariance of the Fierz-Pauli mass term by introducing four scalar fields which preserve a certain internal symmetry in their configuration space. It is then apparent that for each given spacetime metric this construction corresponds to a completely different generally covariant massive gravity theory with different symmetries. The proposed approach is verified by explicit analysis of the physical degrees of freedom of m…
Gravitational backgrounds, such as black holes, AdS, de Sitter and inflationary universes, should be viewed as composite of N soft constituent gravitons. It then follows that such systems are close to quantum criticality of graviton Bose-gas to Bose-liquid transition. Generic properties of the ordinary metric description, including geodesic motion or particle-creation in the background metric, emerge as the large-N limit of quantum scattering of constituent longitudinal gravitons. We show that this picture correctly accounts for physics of large and small black holes in AdS, as well as reprodu…
The description of black holes in loop quantum gravity is a hard and tricky task. In this article, we focus on a minisuperspace approach based on a polymerization procedure. We consider the resulting effective metric and study the propagation of quantum fields in this background. The cross sections for scalar particles and fermions are explicitly calculated. The Teukolsky-Chandrasekhar procedure used to derived the fermionic radial equation of motion for usual spacetimes is entirely generalized to a much larger class. The resulting radial equation can be used in quite a lot of other contexts.
We develop the complete composite theory of gravity, in which the gauge vector fields of the Yang-Mills theory with Lorentz symmetry group are expressed in terms of the tetrad variables obtained from the decomposition of a metric. A key element of a compelling formulation of composite gravity are refined coordinate conditions that offer a natural coupling of the gravitational field to matter and ensure the closest relationship to general relativity. The composite theory of gravity is presented from three different perspectives highlighting its intuitive interpretation, its relationship to gene…
Model of noncommutative gravity is constructed by means of Fedosov deformation quantization of endomorphism bundle. The fields describing noncommutativity -- symplectic form and symplectic connection -- are dynamical, and the resulting theory is completely coordinate covariant and background independent. Its interpretation in terms of Seiberg-Witten map is provided. Also, new action for ordinary (commutative) general relativity is given, which in the present context appears as a commutative limit of noncommutative theory.
In this paper, we extend the work on the AdS/QCD model to quadratic gravity to gain insight into the influence of gravity. We obtain an anisotropic black brane solution to a $5D$ Einstein-Gauss-Bonnet-two Maxwell-dilaton system. The background is specified by an arbitrary exponent, a dilaton field, a time component of the first Maxwell field, and a magnetic component of the second Maxwell field. The system in three cases has been investigated and in each case the effect of the parameter of theory, the anisotropic parameter has been considered. The blackening function supports the thermodynamic…
We study the dynamics of a modified-gravity theory, which is supplemented by an extended Gibbons-Hawking-York boundary term and incorporates diffeomorphism violation through nondynamical background fields denoted as $u$ and $s^{μν}$ in the literature. An ADM decomposition allows us to project the modified Einstein equations into purely spacelike hypersurfaces, which implies the field equations for the induced dynamical three-metric. We also obtain the Hamilton-Jacobi equations of motion for the canonical variables of the theory based on its Hamiltonian, which was derived in a previous work. Th…
In Article I, a harmonic-oscillator model of a universe of n quarks is infinitesimally modified to eliminate the background reference frame. As a result, quark trajectories exhibit the unification of gravity and the harmonic oscillator near the horizon of a quantum black hole, a region that is approximately flat in space-time. Constituent quarks are confined to composite particles by cluster decomposition rather than a binding force. Here, the composite-particles are input for a perturbation model of particle-exchange interactions. As in Article I, the Hamiltonian cannot be expressed as H=H0+H…
We consider the model of modified gravity with dynamical torsion. This model was found to have promising stability properties about various backgrounds. The model admits a self-accelerating solution. We have shown previously that if the parameters are adjusted in such a way that the torsion is much greater than the effective cosmological constant, the self-accelerating solution is unstable: there are exponentially growing modes. Here we study the scalar perturbations in the case when the torsion is of the order of the effective cosmological constant. We find that there are no exponential insta…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a novel, background independent non-perturbative formulation of quantum gravity. We invoke a quantum version of the equivalence principle, which requires both the statistical and symplectic geometries of canonical quantum theory to be fully dynamical quantities. Our approach sheds new light on such basic issues of quantum gravity as the nature of observables, the…
We consider the effective stress-energy tensors for the foreground and background sectors in ghost-free bimetric gravity. By considering the symmetries of the theory, we show that the foreground and background null energy conditions (NECs) are strongly anti-correlated. In particular, the NECs can only be simultaneously fulfilled when they saturate, corresponding to foreground and background cosmological constants. In all other situations, either the foreground or the background is subject to a NEC-violating contribution to the total stress-energy.
The second order perturbation calculations for gravity wave and Einstein equation for space time and matter are presented for the FRW metric cosmological model. While exact equations are found, suitable approximations are made to obtain definite results. In the gravity wave case the small wavelength case allows nearly locally flat background for obtaining a fit to the WMAP data. In the density and curvature case the FRW background is retained for the length scale of WMAP. Clustering and inhomogeneity are understood. The gravity wave ripples from Big Bang couple nonlinearly and redistribute the…
We propose that string theory in the background of dyon black holes in four-dimensional anti-de Sitter spacetime is holographic dual to conformally invariant composite Dirac fermion metal. By utilizing S-duality map, we show that thermodynamic and transport properties of the black hole match with those of composite fermion metal, exhibiting Fermi liquid-like. Built upon Dirac-Schwinger-Zwanziger quantization condition, we argue that turning on magnetic charges to electric black hole along the orbit of Gamma(2) subgroup of SL(2,Z) is equivalent to attaching even unit of statistical flux quanta …
We argue that the demand of background independence in a quantum theory of gravity calls for an extension of standard geometric quantum mechanics. We discuss a possible kinematical and dynamical generalization of the latter by way of a quantum covariance of the state space. Specifically, we apply our scheme to the problem of a background independent formulation of Matrix Theory.
In de Rham-Gabadadze-Tolley (dRGT) massive gravity and bigravity, a non-minimal matter coupling involving both metrics generically re-introduces the Boulware--Deser (BD) ghost. A non-minimal matter coupling via a simple, yet specific composite metric has been proposed, which eliminates the BD ghost below the strong coupling scale. Working explicitly in the metric formulation and for arbitrary spacetime dimensions, we show that this composite metric is the unique consistent non-minimal matter coupling below the strong coupling scale, which emerges out of two diagnostics, namely, absence of Ostr…
Scalar fields in curved backgrounds are assumed to be composite objects. As an example realizing such a possibility we consider a model of the massless tensor field $l_{μν}(x)$ in a 4-dim. background $g_{μν}(x)$ with spontaneously broken Weyl and scale symmetries. It is shown that the potential of $l_{μν}$, represented by a scalar quartic polynomial, has the degenerate extremal described by the composite Nambu-Goldstone scalar boson $ϕ(x):=g^{μν}l_{μν}$. Removal of the degeneracy shows that $ϕ$ acquires a non-zero vev $\langleϕ\rangle_{0}=μ$ which, together with the free parameters of the pote…
