Quantum Gravity Research Articles

Matching the Vilkovisky–DeWitt Effective Action of Quantum Gravity to String Theory

AbstractIn this work, the matching of the Vilkovisky–DeWitt effective action of quantum gravity is discussedwith an example of an ultra‐violet complete theory of quantum gravity. The authors show how this matching enables a calculation of the local Wilson coefficients of the effective action. Several examples in string theory are provided. Moreover, the matching conditions within the context of the swampland program are discussed.

Random matrix model of the Virasoro minimal string

The model of two dimensional quantum gravity defining the Virasoro minimal string, presented recently by Collier, Eberhardt, Mühlmann, and Rodriguez, was also shown to be perturbatively (in topology) equivalent to a random matrix model. An alternative definition is presented here, in terms of double-scaled orthogonal polynomials, thereby allowing direct access to nonperturbative physics. Already at leading order, the defining string equation’s properties yield valuable information about the nonperturbative fate of the model, confirming that the case (c=25,c^=1) (central charges of spacelike and timelike Liouville sectors) is special, by virtue of sharing certain key features of the N=1 supersymmetric JT gravity string equation. Solutions of the full string equation are constructed using a special limit, and the (Cardy) spectral density is completed to all genus and beyond. The distributions of the underlying discrete spectra are readily accessible too, as is the spectral form factor. Some examples of these are exhibited. Published by the American Physical Society 2024

Quantum Field Theory of Black Hole Perturbations with Backreaction: I General Framework

In a seminal work, Hawking showed that natural states for free quantum matter fields on classical spacetimes that solve the spherically symmetric vacuum Einstein equations are KMS states of non-vanishing temperature. Although Hawking’s calculation does not include the backreaction of matter on geometry, it is more than plausible that the corresponding Hawking radiation leads to black hole evaporation which is, in principle, observable. Obviously, an improvement of Hawking’s calculation including backreaction is a problem of quantum gravity. Since no commonly accepted quantum field theory of general relativity is available yet, it has been difficult to reliably derive the backreaction effect. An obvious approach is to use the black hole perturbation theory of a Schwarzschild black hole of fixed mass and to quantize those perturbations. However, it is not clear how to reconcile perturbation theory with gauge invariance beyond linear perturbations. In recent work, we proposed a new approach to this problem that applies when the physical situation has an approximate symmetry, such as homogeneity (cosmology), spherical symmetry (Schwarzschild), or axial symmetry (Kerr). The idea, which is surprisingly feasible, is to first construct the non-perturbative physical (reduced) Hamiltonian of the reduced phase space of fully gauge invariant observables and only then apply perturbation theory directly in terms of observables. The task to construct observables is then disentangled from perturbation theory, thus allowing to unambiguously develop perturbation theory to arbitrary orders. In this first paper of the series we outline and showcase this approach for spherical symmetry and second order in the perturbations for Einstein–Klein–Gordon–Maxwell theory. Details and generalizations to other matter and symmetry and higher orders will appear in subsequent companion papers.

Continuation of Bianchi spacetimes through the big bang

In this paper we present a framework in which the relational description of general relativity can be used to smoothly continue cosmological dynamical systems through the big bang without invoking quantum gravity effects. Cosmological spacetimes contain as a key dynamical variable a notion of scale through the volume factor ν. However, no cosmological observer is ever able to separate their measuring apparatus from the system they are measuring, in that sense every measurement is a relative one, and measurable dynamical variables are, in fact, dimensionless ratios. This is manifest in the identification of a scaling symmetry or “dynamical similarity” in the Einstein-Hilbert action associated with the volume factor. By quotienting out this scaling symmetry, we form a relational system defined on a contact manifold whose dynamical variables are decoupled from scale. When the phase space is reduced to shape space, we show that there exists unique solutions to the equations of motion that pass smoothly through the initial cosmological singularity in flat Friedmann-Lemaître-Robertson-Walker, Bianchi I, and Quiescent Bianchi IX cosmologies. Published by the American Physical Society 2024

Metrics and geodesics on fuzzy spaces

Abstract We study the fuzzy spaces (as special examples of noncommutative manifolds) with their quasicoherent states in order to find their pertinent metrics. We show that they are naturally endowed with two natural “quantum metrics” which are associated with quantum fluctuations of “paths”. The first one provides the length the mean path whereas the second one provides the average length of the fluctuated paths. Onto the classical manifold associated with the quasicoherent state (manifold of the mean values of the coordinate observables in the state minimising their quantum uncertainties) these two metrics provides two minimising geodesic equations. Moreover, fuzzy spaces being not torsion free, we have also two different autoparallel geodesic equations associated with two different adiabatic regimes in the move of a probe onto the fuzzy space. We apply these mathematical results to quantum gravity in BFSS matrix models, and to the quantum information theory of a controlled qubit submitted to noises of a large quantum environment.

Ultraviolet finite resummation of perturbative quantum gravity

Abstract If the metric is chosen to depend exponentially on the conformal factor, and if one works in a gauge where the conformal factor has the wrong sign propagator, perturbative quantum gravity corrections can be partially resummed into a series of terms each of which is ultraviolet finite. These new terms however are not perturbative in some small parameter, and are not individually BRST invariant, or background diffeomorphism invariant. With appropriate parametrisation, the finiteness property holds true also for a full phenomenologically relevant theory of quantum gravity coupled to (beyond the standard model) matter fields, provided massive tadpole corrections are set to zero by a trivial renormalisation.

Quantum and classical properties of the universe according to unimodular quantum cosmology

Abstract We investigate the dynamical behaviour of wavepacket solutions due to unimodular quantum cosmology. We find early and late time quantum eras of the universe.
An Ehrenfest theorem ensures quasi-classical behaviour for the late time universe if the quantum uncertainties are small. The surprising prediction of late time quantum effects for a flat, homogeneous and isotropic universe with a scalar field with an exponential potential is obtained by the analysis of the uncertainty dynamics using the results of the corresponding classical dynamical system. Furthermore quantum correction terms to the Hubble parameter and the matter density are derived. A positive matter expectation value for the de-Sitter universe raises the question if correction terms due to quantum gravity could contribute to solve the dark matter problem.

Loop quantum gravity effects on electromagnetic properties of charged leptons

The efforts in this contribution consist in reassessing a modified Dirac equation that incorporates a γ0γ5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma ^0 \\gamma _5$$\\end{document}-Lorentz-symmetry violating (LSV) term induced as a Loop Quantum Gravity (LQG) effect. Originally, this equation has been applied and considered as a good scenario for describing a number of investigations on the flight time of cosmic neutrinos, which suggests that the speed, in vacuum, in connection with the geometry that describes a granular space-time, takes the energy-dependent form, e.g., v(E)=1±E/ELSV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$v(E) =1 \\pm E/E_{\ ext {\ iny LSV}}$$\\end{document}, with ELSV≈6,5×1017\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{\ ext {\ iny LSV}} \\approx 6,5 \ imes 10^{17}$$\\end{document} GeV for neutrinos. Once LQG provides a viable way to understand this picture consistently, we pursue an analysis of this effective Dirac equation to inspect some of its properties. These include: the derivation of the modified fermionic propagator, attainment of the Gordon decomposition of the vector current with minimal electromagnetic coupling to obtain information on the form factors, examination of the non-relativistic limit of the equation, evaluation of the spin- and velocity-dependent corrections to the Coulomb potential due to LQG effects, and the modified Hamiltonian in the low-relativistic regime. The study of the form factors may open up paths to set up bounds on the LQG parameters from the precision measurements of electromagnetic attributes of the charged leptons, such as their respective electric and magnetic dipole moments.

Divergent features of collective gravitational quantum excitations

In this research, we study different aspects of collective gravitational quantum excitations in the framework of the quantum multistream model. The energy dispersion of collective electrostatic (plasmon) and gravitational excitations or as we call gravity quasiparticle (GQ) are derived using the nonrelativistic and relativistic models and many parameters such as the effective mass, phase, and group speed of quasiparticle excitations are studied, in detail. It is shown that, unlike plasmons with a forbidden energy gap, all positive and negative energy values are allowed for GQs. However, unlike plasmon with a dual-tone nature of collective excitations, the GQs are found to be single-tone with either wave-like or particle-like oscillations being strongly damped. The linear phase-space evolution of GQs indicates that they evolve similarly to the classical system of particles in the center of the mass frame in which the force due to self-consistent gravitational potential plays the role of interparticle forces. It is shown that the damping of wavelike or particle-like excitations in GQ energy dispersion leads to three distinct phenomena of gravitational expansion (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E>0$$\\end{document}), stable matter (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E=0$$\\end{document}) and gravitational collapse (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E<0$$\\end{document}), respectively. The Hubble-Lemaitre-like relation is obtained from the generalized probability current for GQs. The quantum gravitational interference effect is also studied.

Characteristic time scales for the geometry transition of a black hole to a white hole from spinfoams

Abstract Quantum fluctuations of the metric may provide a decay mechanism for black holes through a transition to a white hole geometry. &amp;#xD;Previous studies formulated Loop Quantum Gravity amplitudes with a view to describe this process. We identify two timescales to be extracted which we call the crossing time and the lifetime and complete a calculation that gives explicit estimates using the asymptotics of the EPRL model. The crossing time is found to scale linearly in the mass, in agreement with previous results by Ambrus and H'aj'i\v{c}ek and more recent results by Barcel'o, Carballo--Rubio and Garay. The lifetime is found to depend instead on the spread of the quantum state, and thus its dependence on the mass can take a large range of values. This indicates that the truncation/approximation used here is not appropriate to estimate this observable with any certainty. The simplest choice of a balanced semiclassical state is shown to yield an exponential scaling of the lifetime in the mass squared. Our analysis only considers 2-complexes without bulk faces, a significant limitation. In particular it is not clear how our estimates will be affected under refinements. This work should be understood as a step towards a fuller calculation in the context of covariant Loop Quantum Gravity.

Constructing all BPS black hole microstates from the gravitational path integral

Understanding how to prepare and count black hole micro-states by using the gravitational path integral is one of the most important problems in quantum gravity. Nevertheless, a state-by-state count of black hole microstates is difficult because the apparent number of degrees of freedom available in the gravitational effective theory can vastly exceed the entropy of the black hole, even in the special case of BPS black holes. In this paper, we show that we can use the gravitational path integral to prepare a basis for the Hilbert space of all BPS black hole microstates. We find that the dimension of this Hilbert space computed by an explicit state count is in complete agreement with the degeneracy obtained from the Gibbons-Hawking prescription. Specifically, this match includes all non-perturbative corrections in 1/GN. Such corrections are, in turn, necessary in order for this degeneracy of BPS states to match the non-perturbative terms in the 1/GN expansion in the string theory count of such microstates.

Analyticity and the Unruh effect: a study of local modular flow

The Unruh effect can be formulated as the statement that the Minkowski vacuum in a Rindler wedge has a boost as its modular flow. In recent years, other examples of states with geometrically local modular flow have played important roles in understanding energy and entropy in quantum field theory and quantum gravity. Here I initiate a general study of the settings in which geometric modular flow can arise, showing (i) that any geometric modular flow must be a conformal symmetry of the background spacetime, and (ii) that in a well behaved class of “weakly analytic” states, geometric modular flow must be future-directed. I further argue that if a geometric transformation is conformal but not isometric, then it can only be realized as modular flow in a conformal field theory. Finally, I discuss a few settings in which converse results can be shown — i.e., settings in which a state can be constructed whose modular flow reproduces a given vector field.

Nonsingular cosmology from nonsupersymmetric AdS instability conjecture

We show that the nonsupersymmetric anti–de Sitter (AdS) instability conjecture can point to how quantum gravity removes the initial big bang singularity, leading to a potential resolution for the past-incomplete inflationary Universe. From the constraints on the dynamics of the Universe realized as the nucleation of a thin-wall bubble mediating the decay of the nonsupersymmetric AdS vacuum, we find the critical temperature Tc and the critical scale factor ac for which the Universe exists. These critical quantities are all finite and determined in terms of the parameters specifying the stringy 10D AdS vacuum solutions. Additionally, we derive the prediction of quantum gravity for Tc and ac relying on the inflationary observations. Published by the American Physical Society 2024

Gravitational corrections to the two-loop beta function in a non-Abelian gauge theory

This paper investigates the coupling of massive fermions to gravity within the context of a non-Abelian gauge theory, utilizing the effective field theory framework for quantum gravity. Specifically, we calculate the two-loop beta function of the gauge coupling constant in a non-Abelian gauge theory, employing the one-graviton exchange approximation. Our findings reveal that gravitational corrections may lead to a nontrivial UV fixed point in the beta function of the gauge coupling constant, contingent upon the specific gauge group and the quantity of fermions involved. Published by the American Physical Society 2024

The Planck Computer Is the Quantum Gravity Computer: We Live inside a Gigantic Computer, the Hubble Sphere Computer?

Recent developments in the quantization of general relativity theory provide a new perspective on matter and even the whole universe. Already, in 1922, Eddington suggested that a future quantum gravity theory had to be linked to Planck length. This is today the main view among many working with quantum gravity. Recently, it has been demonstrated how Planck length, the Planck time, can be extracted from gravity observations with no knowledge of G, ℏ, or even c. Rooted in this, both general relativity theory and multiple other gravity theories can be quantized and linked to the Planck scale. A revelation from this is that matter seems to be ticking at the reduced Compton frequency, where each tick can be seen as one bit, and one bit corresponds to a Planck mass event. This new speculative way of looking at gravity can also potentially tell us considerably about what quantum gravity computers are and what they potentially can do. We will conjecture that that all quantum gravity and quantum gravity computers are directly linked to the Planck scale and the Compton frequency in matter, something we will discuss in this paper. Quantum gravity computers, we will see, in many ways, are nature’s own designed computers with enormous capacity to 3D “print” real time. So, somewhat speculatively, we suggest we live inside a gigantic quantum gravity computer known as the Hubble sphere, and we even are quantum gravity computers. The observable universe is based on this model, basically a quantum gravity computer that calculates approximately 10104 bits per second (bps).

Quantum geometric perspective on the origin of quantum-conditioned curvatures

Abstract The quantization of the gravitational field, which includes the metric field, has been investigated using various methods such as loop quantum gravity, quantum field theory, and string theory. Nevertheless, an alternative strategy to tackle the challenge of merging the fundamentally different theories of general relativity (GR) and quantum mechanics (QM) is through a quantum geometric approach. This particular approach entails extending QM to relativistic energies and finite gravitational fields, while also expanding the continuous Riemann to a discretized (quantized) Finsler-Hamilton geometry. By embracing this method, it may be feasible to bridge the gap between GR and QM or even achieve their unification. The resulting fundamental tensor appears to blend its original classical and quantum characteristics, effectively integrating quantum-mechanically induced revisions to the affine connections and spacetime curvatures. Our study primarily focuses on investigating the Ricci curvature tensor in the context of the Einstein-Gilbert-Straus metric. By employing both analytical and numerical methods, we have identified quantum-conditioned curvatures (QCC) that act as additional sources of gravitation. These QCC exhibit a fundamental difference from the traditional curvatures described by Einsteinian GR. While the Ricci curvatures are predominantly positive across most regions, the quantized Ricci curvatures display negativity. We conclude that the QCC a) possess an intrinsic, essential, and real character, b) should not be disregarded due to their significant magnitude, and c) are fundamentally different from the curvatures found in classical GR. Moreover, we conclude that the proposed quantum geometric approach may offer an alternative mathematical framework for understanding the emergence of quantum gravity.

Waiting for inflation: A new initial state for the Universe

We propose a cosmological lingering phase for the initial state prior to inflation which would help address the singularity problem of inflation. The Universe begins with a constant (Hagedorn) temperature and then transitions into an inflationary universe while preserving the null energy condition (NEC). We first consider the phase space of positive spatial curvature models within general relativity and with matter sources that respect the NEC. Depending on the duration of the postlingering inflation, these models can produce a small amount of observable spatial curvature in the cosmic microwave background. We also discuss how lingering can arise with or without spatial curvature in theories of quantum gravity when considering the thermodynamic scaling of particles and its impact on the early Universe. The string theory dilaton is essential to the dynamics. There are many open questions that remain. Published by the American Physical Society 2024

Minimal-length quantum field theory: a first-principle approach

Phenomenological models of quantum gravity often consider the existence of some form of minimal length. This feature is commonly described in the context of quantum mechanics and using the corresponding formalism and techniques. Although few attempts at a quantum field-theoretical description of a minimal length has been proposed, they are rather the exception and there is no general agreement on the correct one. Here, using the quantum-mechanical model as a guidance, we propose a first-principle definition of a quantum field theory including a minimal length. Specifically, we propose a two-step procedure, by first describing the quantum-mechanical models as a classical field theory and subsequently quantizing it. We are thus able to provide a foundation for further exploration of the implications of a minimal length in quantum field theory.

Open AdS/CFT via a double-trace deformation

A concrete model of extracting the physics from the bulk of a gravitational universe is important to the study of quantum gravity and its possible relationship with experiments. Such a model can be constructed in the AdS/CFT correspondence by gluing a bath on the asymptotic boundary of the bulk anti-de Sitter (AdS) spacetime. This bath models a laboratory and is described by a quantum field theory. In the dual conformal field theory (CFT) description this coupling is achieved by a double-trace deformation that couples the CFT with the bath. This suggests that the physics observed by the laboratory is fully unitary. In this paper, we analyze the quantum aspects of this model in detail which conveys new lessons about the AdS/CFT correspondence, and we discuss the potential usefulness of this model in understanding subregion physics in a gravitational universe.

Conformal symmetry in quantum gravity

We study the problem of how to derive conformal symmetry in the framework of quantum gravity. We start with a generic gravitational theory which is invariant under both the general coordinate transformation (GCT) and Weyl transformation (or equivalently, local scale transformation), and then construct its BRST formalism by fixing the gauge symmetries by the extended de Donder gauge and scalar gauge conditions. These gauge-fixing conditions are invariant under global GL(4) and global scale transformations. The gauge-fixed and BRST invariant quantum action possesses a huge Poincaré-like IOSp(10|10) global symmetry, from which we can construct an extended conformal symmetry in a flat Minkowski background in the sense that the Lorentz symmetry is replaced with the GL(4) symmetry. Moreover, we construct the conventional conformal symmetry out of this extended symmetry. With a flat Minkowski background ⟨gμν⟩=ημν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle g_{\\mu \ u } \\rangle = \\eta _{\\mu \ u }$$\\end{document} and a non-zero scalar field ⟨ϕ⟩≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle \\phi \\rangle \ e 0$$\\end{document}, the GL(4) and global scale symmetries are spontaneously broken to the Lorentz symmetry, thereby proving that the graviton and the dilaton are respectively the corresponding Nambu–Goldstone bosons, and therefore they must be exactly massless at nonperturbative level. One of remarkable aspects in our findings is that in quantum gravity, a derivation of conformal symmetry does not depend on a classical action, and its generators are built from only the gauge-fixing and the FP ghost actions. Finally, we address a generalized Zumino theorem in quantum gravity.