Search

Recently, it was shown that if two distant test masses, each in a spatially superposed quantum state, become entangled due to their mutual gravitational interaction, then this entanglement could serve as evidence of the quantum nature of gravity. We extend this treatment to a many-body system in a general setup and study the entanglement properties of the time-evolved state. We exactly compute the time-dependent I-concurrence for every bipartition and obtain the necessary and sufficient condition for the creation of genuine many-body entanglement. We further show that this entanglement is of generalised GHZ type when certain conditions are met. We also evaluate the amount of multipartite entanglement in the system using a set of generalised Meyer-Wallach measures. [ABSTRACT FROM AUTHOR]

We extend the analytic description of complex no-boundary solutions in the context of inflation to large field models. We discuss the Kontsevich–Segal–Witten (KSW) criterion and find it is satisfied in small field models, while in large field models it depends on an integral involving V ′ (ϕ) over the range of inflation. It follows that although particular models are ruled out, e.g. quadratic inflation, the criterion does not truly constrain inflationary phenomenology since any inflation potential can be completed beyond observable scales so as to satisfy KSW. [ABSTRACT FROM AUTHOR]

We point out that dark matter and dark energy arise naturally in a recently proposed model of combinatorial quantum gravity. Dark energy is due to the ground-state curvature at finite coupling, dark matter arises from allotropy in the discrete structure of space-time. The stable structure of the space-time 'crystal' represents the curved background, the coexisting metastable allotropes of higher curvature and energy are natural candidates for dark matter. We thus suggest that dark energy and dark matter are two manifestation of quantum gravity. [ABSTRACT FROM AUTHOR]

This study aims to provide general axioms that should hold for any theory of quantum gravity. These axioms imply that spacetime is an emergent structure, which emerges from information. This information cannot occur in spacetime, as spacetime emerges from it, and hence exists in an abstract mathematical Platonic realm. Thus, quantum gravity exists as a formal system in this Platonic realm. Gödel’s theorems apply to such formal systems, and hence they apply to quantum gravity. This limits the existence of a complete consistent theory of quantum gravity. However, we generalize the Lucas-Penrose argument and argue that a non-algorithmic understanding exists in this Platonic realm. It makes it possible to have a complete and consistent theory of quantum gravity. [ABSTRACT FROM AUTHOR]

In this paper, we consider the single-parameter ℛ+cℛ2 gravitational action and use constraints from astrophysics and the laboratory to derive a natural relation between the coefficient c and the value of the cosmological constant. We find that the renormalization of c from the energy of the inflationary phase to the infrared, where the acceleration of the expansion of the universe takes place, is correlated with the evolution of the vacuum energy. Our results suggest that the coefficient of the ℛ2 term may provide an unexpected bridge between high-energy physics and cosmological phenomena such as inflation and dark energy. [ABSTRACT FROM AUTHOR]

The question about the appearance of time in the semiclassical limit of quantum gravity continues to be discussed in the literature. It is believed that a temporal Schrödinger equation for matter fields on the background of a classical gravitational field must be true. To obtain this equation, the Born–Oppenheimer approximation for gravity is used. However, the origin of time in this equation is different in works of various authors. For example, in the papers of Kiefer and his collaborators, time is a parameter along a classical trajectory of gravitational field; in the works of Montani and his collaborators, the origin of time is introducing the Kuchař–Torre reference fluid; in the extended phase space approach, the origin of time is the consequence of existing of the observer in a fixed reference frame. We discuss and compare these approaches. To make the calculations transparent, we illustrate them with the model of a closed isotropic universe. In each approach, one obtains some Schrödinger equation for matter fields with quantum gravitational corrections, but the form of the equation and the corrections depend on additional assumptions which are rather arbitrary. None of the approaches can explain how time had appeared in the Early Universe, since it is supposed that classical gravity and, therefore, classical spacetime had already come into being. [ABSTRACT FROM AUTHOR]

In this essay, we argue that certain aspects of the measurement require revision in Quantum Gravity. Using entropic arguments, we propose that the number of measurement outcomes and the accuracy (or the range) of the measurement are limited by the entropy of the black hole associated with the observer’s scale. This also implies the necessity of modifying the algebra of commutation relationships to ensure a finite representation of observables, changing the Heisenberg Uncertainty Principle in this manner. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Several approaches to quantum gravity lead to nonlocal modifications of fields' dynamics. This, in turn, can give rise to nonlocal modifications of quantum mechanics at non-relativistic energies. Here, we analyze the nonlocal Schrödinger evolution of a quantum harmonic oscillator in one such scenario, where the problem can be addressed without the use of perturbation theory. We demonstrate that although deviations from standard quantum predictions occur at low occupation numbers, where they could potentially be detected or constrained by high-precision experiments, the classical limits of quantum probability densities and free energy remain unaffected up to energies comparable with the nonlocality scale. These results provide an example of nonlocal quantum dynamics compatible with classical predictions, suggesting massive quantum objects as a promising avenue for testing some phenomenological aspects of quantum gravity. [ABSTRACT FROM AUTHOR]

In this paper, we address a theoretical investigation of the gravitational lensing phenomenon within the space-time framework of a holonomy-corrected spherically symmetric black hole (BH), incorporating both ordinary and phantom global monopoles. Our focus lies on the analysis of null geodesics within this BH background, examining the influence of ordinary and phantom global monopoles on the effective potential of null geodesics of the system. Afterwards, we derive analytical expressions for the deflection angle of photon light, considering weak field limit. The obtain expressions are presented up to the second order of the Loop Quantum Gravity parameter, enabling a thorough examination of the impact of ordinary and phantom global monopoles on the deflection angle. [ABSTRACT FROM AUTHOR]

Both the Barrow and Tsallis δ entropies are one-parameter generalizations of the black-hole entropy, with the same microcanonical functional form. The ensuing deformation is quantified by a dimensionless parameter Δ , which in the case of Barrow entropy represents the anomalous dimension caused by quantum fluctuations over the horizon surface, while in Tsallis' case, it describes the deviation of the holographic scaling from extensivity. Here, we utilize the gravity-thermodynamics conjecture with the Barrow–Tsallis entropy to investigate the implications of the related modified Friedmann equations on the spectrum of primordial gravitational waves. We show that, with the experimental sensitivity of the next generation of gravitational wave detectors, such as the Big Bang Observer, it will be possible to discriminate deviations from the Λ CDM model up to Δ ≲ O (10 - 3) . In this limit, Barrow–Tsallis entropy reduces to a logarithmic correction to holographic scaling, which is nearly universally predicted by both entanglement entropy calculations in the UV regime and by several candidate theories of quantum gravity. Hence, our considerations and results are expected to have general validity in the quantum gravity framework. [ABSTRACT FROM AUTHOR]

We study the behavior of static, spherically symmetric solutions to the field equations of scalar–tensor theories (STT) of gravity belonging to the Bergmann–Wagoner–Nordtvedt class, in the presence of an electric and/or magnetic charge. This class of theories includes the Brans–Dicke, Barker and Schwinger STT as well as nonminimally coupled scalar fields with an arbitrary parameter ξ . The study is restricted to canonical (nonphantom) versions of the theories and scalar fields without a self-interaction potential. Only radial (monopole) perturbations are considered as the most likely ones to cause an instability. The static background solutions contain naked singularities, but we formulate the boundary conditions in such a way that would preserve their meaning if a singularity is smoothed, for example, due to quantum gravity effects. These boundary conditions look more physical than those used by other authors. Since the solutions of all STT under study are related by conformal transformations, the stability problem for all of them reduces to the same wave equation, but the boundary conditions for perturbations (and sometimes the boundaries themselves) are different in different STT, which affects the stability results. The stability or instability conclusions are obtained for different branches of solutions in the theories under consideration and are presented in a table form. [ABSTRACT FROM AUTHOR]

It is often argued that the Planck length (or mass) is the scale of quantum gravity, as shown by comparing the Compton length with the gravitational radius of a particle. However, the Compton length is relevant in scattering processes but does not play a significant role in bound states. We will derive a possible ground state for a dust ball composed of a large number of quantum particles entailing a core with the size of a fraction of the horizon radius. This suggests that quantum gravity becomes physically relevant for systems with compactness of order one for which the nonlinearity of General Relativity cannot be discarded. A quantum corrected geometry can then be obtained from the effective energy-momentum tensor of the core or from quantum coherent states for the effective gravitational degrees of freedom. These descriptions replace the classical singularity of black holes with integrable structures in which tidal forces remain finite and there is no inner Cauchy horizon. The extension to rotating systems is briefly mentioned. [ABSTRACT FROM AUTHOR]

Classical General Relativity is a dynamical theory of spacetime metrics of Lorentzian signature. In particular the classical metric field is nowhere degenerate in spacetime. In its initial value formulation with respect to a Cauchy surface the induced metric is of Euclidian signature and nowhere degenerate on it. It is only under this assumption of non-degeneracy of the induced metric that one can derive the hypersurface deformation algebra between the initial value constraints which is absolutely transparent from the fact that the inverse of the induced metric is needed to close the algebra. This statement is independent of the density weight that one may want to equip the spatial metric with. Accordingly, the very definition of a non-anomalous representation of the hypersurface deformation algebra in quantum gravity has to address the issue of non-degeneracy of the induced metric that is needed in the classical theory. In the Hilbert space representation employed in Loop Quantum Gravity (LQG) most emphasis has been laid to define an inverse metric operator on the dense domain of spin network states although they represent induced quantum geometries which are degenerate almost everywhere. It is no surprise that demonstration of closure of the constraint algebra on this domain meets difficulties because it is a sector of the quantum theory which is classically forbidden and which lies outside the domain of definition of the classical hypersurface deformation algebra. Various suggestions for addressing the issue such as non-standard operator topologies, dual spaces (habitats) and density weights have been proposed to address this issue with respect to the quantum dynamics of LQG. In this article we summarise these developments and argue that insisting on a dense domain of non-degenerate states within the LQG representation may provide a natural resolution of the issue thereby possibly avoiding the above mentioned non-standard constructions. [ABSTRACT FROM AUTHOR]

General relativity (GR) in its current classical formulation is fundamentally different from quantum mechanics (QM). We argue that the everlasting battle for exploring and understanding the Universe and then privileging a consistent perception of reality is therefore awaiting a consolidator rather than a conqueror. This should be capable of either unifying these two different benchmarks or at least bringing one closer to another! The latter conservatively describes the consolidating quantum geometric approach, which combines generalization of QM to relativistic energies and gravitational fields and continuous Riemann to discretized Finsler geometry. We found that this type of quantum geometric approach seems to unveil additional quantum-conditioned spacetime curvatures (QCC), sources of gravitation), which obviously could not be disclosed in Einstein's GR, especially at large scales. This study introduces analytical and numerical analyses of QCC. We conclude that (i) nature and characteristics of QCC are fundamentally distinguishable from the classical GR's spacetime curvatures, (ii) the QCC are intrinsic, real and essential, i.e. not artifacts that would be removed in a certain coordinate transformation and (iii) the magnitude of QCC are nonnegligible to be underestimated. We also conclude that the spacetime at quantum scales seems to be no longer smooth or continuous so that the proposed quantum geometric approach would be regarded as a novel mathematical framework for the emergence of quantum gravity. Last but not least, a maximal proper force is predicted as a new physical constant, which is responsible for the maximal and gravitational acceleration of a quantum particle that would live in the emerged spacetime curvatures. Thereby, the quantum geometric nature of QCC can be accessed and assessed. [ABSTRACT FROM AUTHOR]

In this paper, we show how the path integral for gravity and matter on a piecewise flat spacetime can be used to define the physical quantum gravity states and the related transition amplitudes. The physical states are given by the path integrals for open manifolds from a certain topological class, while the corresponding transition amplitudes are obtained by gluing two such open manifolds into a closed one and calculating the corresponding path integral. We also solve the problem of how to associate a quantum gravity state to an effective action. This is done by using the path integral for a closed manifold from the transition-amplitude topological class so that the state which corresponds to the effective action can be chosen to be the Hartle–Hawking or the Vilenkin wavefunction for the vacuum manifold component of the transition-amplitude manifold. [ABSTRACT FROM AUTHOR]

In this paper, we systematically study the evolution of the Universe within the framework of a modified loop quantum cosmological model (mLQC-I) using various inflationary potentials, including chaotic, Starobinsky, generalized Starobinsky, polynomials of the first and second kinds, generalized T-models and natural inflation. In all these models, the big bang singularity is replaced by a quantum bounce, and the evolution of the Universe, both before and after the bounce, is universal and weakly dependent on the inflationary potentials, as long as the evolution is dominated by the kinetic energy of the inflaton at the bounce. In particular, the pre-bounce evolution can be universally divided into three different phases: pre-bouncing, pre-transition, and pre-de Sitter. The pre-bouncing phase occurs immediately before the quantum bounce, during which the evolution of the Universe is dominated by the kinetic energy of the inflaton. Thus, the equation of state of the inflaton is about one, w (ϕ) ≃ 1 . Soon, the inflation potential takes over, so w (ϕ) rapidly falls from one to negative one. This pre-transition phase is very short and quickly turns into the pre-de Sitter phase, whereby the effective cosmological constant of Planck size takes over and dominates the rest of the contracting phase. Throughout the entire pre-bounce regime, the evolution of both the expansion factor and the inflaton can be approximated by universal analytical solutions, independent of the specific inflation potentials. [ABSTRACT FROM AUTHOR]

Integrating loop quantum gravity with classical gravitational collapse models offers an effective solution to the black hole singularity problem and predicts the formation of a white hole in the later stages of collapse. Furthermore, the quantum extension of Kruskal spacetime indicates that white holes may convey information about earlier companion black holes. Photons emitted from the accretion disks of these companion black holes enter the black hole, traverse the highly quantum region, and then re-emerge from white holes in our universe. This process enables us to observe images of the companion black holes' accretion disks, providing insights into quantum gravity. In our study, we successfully obtained these accretion disk images. Our results indicate that these accretion disk images are confined within a circle with a radius equal to the critical impact parameter, while traditional accretion disk images are typically located outside this circle. As the observational angle increases, the accretion disk images transition from a ring shape to a shell-like shape. Furthermore, the positional and width characteristics of these accretion disk images are opposite to those of traditional accretion disk images. These findings provide valuable references for astronomical observations aimed at validating the investigated quantum gravity model. [ABSTRACT FROM AUTHOR]

The Moyal-Higher-Spin (MHS) formalism, involving fields dependent on spacetime and auxiliary coordinates, is an approach to studying higher-spin (HS)-like models. To determine the particle content of the MHS model of the Yang–Mills type, we calculate the quartic Casimir operator for on-shell MHS fields, finding it to be generally non-vanishing, indicative of infinite/continuous spin degrees of freedom. We propose an on-shell basis for these infinite/continuous spin states. Additionally, we analyse the content of a massive MHS model. [ABSTRACT FROM AUTHOR]

From a dynamical systems point of view, a trivalent spin network model in Loop Quantum Gravity is considered, which presents self‐organized criticality (SOC), arising from a spin propagation dynamics. A partition function is obtained for the domains of stability connecting gauge non‐invariant avalanches, leading to an entropy formula for the asymptotic SOC state. The microscopic origin of this SOC entropy is therefore given by the excitation‐relaxation spin dynamics in the avalanche cycle. The puncturing of trivalent spin networks (TSN) edges participating in the avalanche are counted in terms of an ensemble perimeter over the implicit avalanches. By identifying this perimeter with that of an isolated (2+1)$(2+1)$‐D black hole horizon, it is conjectured that the SOC entropy reduces to the Bekenstein‐Hawking perimeter‐entropy law for the Bañados, Teitelboim, and Zanelli (BTZ) black hole, by an appropriate adjustment of a potential function based on the thermodynamical formalism of Sinai, Ruelle, and Bowen. [ABSTRACT FROM AUTHOR]

Chiral torsional anomalies have recently been applied in condensed matter and models of gravitation and quantum field theory, in particular in Dirac and Weyl materials. Moreover, Einstein–Cartan space–time elastic gauge spaces with vanishing spin connection have appeared in the teleparallelism framework. Recently, Ciappina et al. (PRD (2020)) have investigated torsion in quantum field theory through time loops on Dirac materials endowed with torsion in (2 + 1)-dimensional space–time where the third dimension is replaced by time dimension. They considered Riemann-flat spaces graphenes for example. In this paper, a space–time teleparallel geometry is used where we encoded physical information of Burgers vectors on Dirac curved materials (GdA, CQG 38 (2021)). It is shown that when the magnetic or pseudo-magnetic field is encoded in this metric one obtains an interesting (2 + 1)-dimensional space–time is shown to lead to pseudo-Maxwell equations. We also show that a Riemann-flat grapheno, for example, imposes a vanishing Nieh–Yan (NY) torsional anomaly, whereas a curved Dirac material presents a non-vanishing NY anomaly. Torsion-induced holonomy on Dirac materials is investigated. Signatures of chiral dynamo effects in Dirac materials from the chiral chemical potential encoded into the covariant derivative are found. It is shown that in the absence of chiral effect the magnetic field torsion contribution decays, whereas in the chiral dynamo case, a dynamo effect is found. It is shown that from the interaction of chiral chemical potential with torsion an effective chiral chemical potential is found, which depends on the zero-component of Cartan torsion. [ABSTRACT FROM AUTHOR]

We revisit the construction of quantum Riemannian geometries on graphs starting from a hermitian metric compatible connection, which always exists. We use this method to find quantum Levi-Civita connections on the n-leg star graph for n = 2 , 3 , 4 and find the same phenomenon as recently found for the A n Dynkin graph that the metric length for each inbound arrow has to exceed the length in the other direction by a multiple, here n . We then study quantum geodesics on graphs and construct these on the 4-leg graph and on the integer lattice line Z with a general edge-symmetric metric. [ABSTRACT FROM AUTHOR]

We survey on-shell and off-shell higher derivative supergravities in dimensions 1 ≤ D ≤ 11. Various approaches to their construction, including the Noether procedure, (harmonic) superspace, superform method, superconformal tensor calculus, S -matrix and dimensional reduction, are summarized. Primarily the bosonic parts of the invariants and the supertransformations of the fermionic fields are provided. The process of going on-shell, solutions to the Killing spinor equations, typical supersymmetric solutions, and the role of duality symmetries in the context of R 4 , D 4 R 4 and D 6 R 4 invariants are reviewed. [ABSTRACT FROM AUTHOR]

We consider an infinite planar Delaunay graph Gϵ which is obtained by locally deforming the coordinate embedding of a general isoradial graph Gcr, with respect to a real deformation parameter ϵ. Using Kenyon's exact and asymptotic results for the critical Green's function on an isoradial graph, we calculate the leading asymptotics of the first- and second-order terms in the perturbative expansion of the log-determinant of the Laplace-Beltrami operator Δ(ϵ), the David-Eynard Kähler operator D(ϵ), and the conformal Laplacian Δ ​(ϵ) on the deformed Delaunay graph Gϵ. We show that the scaling limits of the second-order bi-local term for both the Laplace-Beltrami and David-Eynard Kähler operators exist and coincide, with a shared value independent of the choice of the initial isoradial graph Gcr. Our results allow us to define a discrete analog of the stress-energy tensor for each of the three operators. Furthermore, we can identify a central charge (c=-2) in the case of both the Laplace-Beltrami and David-Eynard Kähler operators. While the scaling limit is consistent with the stress-energy tensor and the value of the central charge for the Gaussian free field (GFF), the discrete central charge value of c=-2 for the David-Eynard Kähler operator is, however, at odds with the value of c=-26 expected by Polyakov's theory of 2D quantum gravity; moreover, there are problems with convergence of the scaling limit of the discrete stress-energy tensor for the David-Eynard Kähler operator. The second-order bi-local term for the conformal Laplacian involves anomalous terms corresponding to the creation of discrete curvature dipoles in the deformed Delaunay graph Gϵ; we examine the difficulties in defining a convergent scaling limit in this case. Connections with some discrete statistical models at criticality are explored. [ABSTRACT FROM AUTHOR]

In 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. [ABSTRACT FROM AUTHOR]

We review Holst formalism and dynamical equivalence with standard GR (in dimension 4). Holst formalism is written for a spin coframe field e μ I and a Spin (3 , 1) -connection ω μ I J on spacetime M and it depends on the Holst parameter γ ∈ ℝ − { 0 }. We show the model is dynamically equivalent to standard GR, in the sense that up to a pointwise Spin (3 , 1) -gauge transformation acting on (uppercase Latin) frame indices, solutions of the two models are in one-to-one correspondence. Hence, the two models are classically equivalent. One can also introduce new variables by splitting the spin connection into a pair of a Spin (3) -connection A μ i and a Spin (3) -valued 1-form k μ i . The construction of these new variables relies on a particular algebraic structure, called a reductive splitting. A weaker structure than requiring that the gauge group splits as the products of two sub-groups, as it happens in Euclidean signature in the selfdual formulation originally introduced in this context by Ashtekar, and it still allows to deal with the Lorentzian signature without resorting to complexifications. The reductive splitting of SL (2 , ℂ) is not unique and it is parameterized by a real parameter β which is called the Immirzi parameter. The splitting is here done on spacetime, not on space as it is usually done in the literature, to obtain a Spin (3) -connection A μ i , which is called the Barbero–Immirzi connection on spacetime. One obtains a covariant model depending on the fields (e μ I , A μ i , k μ i) which is again dynamically equivalent to standard GR. Usually in the literature one sets β = γ for the sake of simplicity. Here, we keep the Holst and Immirzi parameters distinct to show that eventually only β will survive in boundary field equations. [ABSTRACT FROM AUTHOR]

A black hole is a mysterious cosmic object that cannot be observed directly, and research on its structure continues with increasing interest today. Investigating the effects on the motion of a half-spin relativistic particle around a black hole may provide us with interesting information. Research on the particle scale requires considering quantum contributions, but a well-established quantum gravity theory has not yet been constructed in literature. In our research, the interaction between the spin of a Dirac particle and the gravitational field is discussed within the scope of the rainbow formalism, which is one of the most studied quantum gravity approaches. [ABSTRACT FROM AUTHOR]

Motivated by conceptual problems in quantum theories of gravity, the gravitational eikonal approach, inspired by its electromagnetic predecessor, has been successfully applied to the transplanckian energy collisions of elementary particles and strings since the late eighties, and to string-brane collisions in the past decade. After the direct detection of gravitational waves from black-hole mergers, most of the attention has shifted towards adapting these methods to the physics of black-hole encounters. For such systems, the eikonal exponentiation provides an amplitude-based approach to calculate classical gravitational observables, thus complementing more traditional analytic methods such as the Post-Newtonian expansion, the worldline formalism, or the Effective-One-Body approach. In this review we summarize the main ideas and techniques behind the gravitational eikonal formalism. We discuss how it can be applied in various different physical setups involving particles, strings and branes and then we mainly concentrate on the most recent developments, focusing on massive scalars minimally coupled to gravity, for which we aim at being as self-contained and comprehensive as possible. [ABSTRACT FROM AUTHOR]

Unifying quantum theory and gravity remains a fundamental challenge in physics. While most existing literature focuses on the ultraviolet modifications of quantum theory due to gravity, this work shows that generic infrared modifications arise when we describe quantum theory in curved spacetime. We explicitly demonstrate that the modifications to the position-momentum algebra are proportional to curvature invariants (such as the Ricci scalar and Kretschmann scalar). Our results, derived through a rigorous application of Dirac's quantization procedure, demonstrate that infrared effects in quantum systems can be axiomatically derived. We study particle dynamics in an arbitrary curved spacetime by embedding them in a higher-dimensional flat geometry. Our approach, which involves embedding particle dynamics in a higher-dimensional flat geometry and utilizing Dirac's quantization procedure, allows us to capture the dynamics of a particle in 4-dimensional curved spacetime through a modified position-momentum algebra. When applied to various spacetimes, this method reveals that the corrections due to the spacetime curvature are universal. We further compare our results with those derived using extended uncertainty principles. Finally, we discuss the implications of our work for black holes and entanglement. [ABSTRACT FROM AUTHOR]

We study how the number of degrees of freedom in Weyl conformal gravity runs with the energy scale from the UV fixed point. To this end we employ two approaches. First, we utilize the Fradkin–Tseytlin prescription for the number of degrees of freedom and demonstrate that the one-loop result is highly dependent on the selected background. We then employ the counting methodology based on the a- and c-function, which are typically used to characterize the trace anomaly of conformal field theories in four dimensions. We compute these in the enhanced one-loop approximation and demonstrate that the degrees of freedom decrease monotonically from six degrees in the UV regime. This behavior is independent of the backgrounds considered. Further salient issues, such as the connection between the Fradkin–Tseytlin prescription and counting based on the a- and c-function, or the applicability of both methods in Einstein's gravity, are also addressed. [ABSTRACT FROM AUTHOR]

After averaging over fermion couplings, SYK has a collective field description that sometimes has "wormhole" solutions. We study the fate of these wormholes when the couplings are fixed. Working mainly in a simple model, we find that the wormhole saddles persist, but that new saddles also appear elsewhere in the integration space — "half-wormholes." The wormhole contributions depend only weakly on the specific choice of couplings, while the half-wormhole contributions are strongly sensitive. The half-wormholes are crucial for factorization of decoupled systems with fixed couplings, but they vanish after averaging, leaving the non-factorizing wormhole behind. [ABSTRACT FROM AUTHOR]

We consider a quantum scalar field in a classical (Euclidean) De Sitter background, whose radius is fixed dynamically by Einstein's equations. In the case of a free scalar, it has been shown by Becker and Reuter that if one regulates the quantum effective action by putting a cutoff N on the modes of the quantum field, the radius is driven dynamically to infinity when N tends to infinity. We show that this result holds also in the case of a self-interacting scalar, both in the symmetric and broken-symmetry phase. Furthermore, when the gravitational background is put on shell, the quantum corrections to the mass and quartic self-coupling are found to be finite. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We present thought experiments to measure the Arnowitt–Deser–Misner E ADM and Bondi–Sachs energy E BS of isolated systems in general relativity. The expression of E BS used in the protocol is likely to have other applications. In particular, it is well-suited to be promoted to an operator in non-perturbative loop quantum gravity. [ABSTRACT FROM AUTHOR]

We consider the discrete Z 4 symmetry i ^ , which takes place in the scenario of quantum gravity where the gravitational tetrads emerge as the order parameter—the vacuum expectation value of the bilinear combination of fermionic operators. Under this symmetry operation, i ^ , the emerging tetrads are multiplied by the imaginary unit, i ^ e μ a = − i e μ a . The existence of such symmetry and the spontaneous breaking of this symmetry are also supported by the consideration of the symmetry breaking scheme in the topological superfluid 3He-B. The order parameter in 3He-B is also the bilinear combination of the fermionic operators. This order parameter is the analog of the tetrad field, but it has complex values. The i ^ -symmetry operation changes the phase of the complex order parameter by π / 2 , which corresponds to the Z 4 discrete symmetry in quantum gravity. We also considered the alternative scenario of the breaking of this Z 4 symmetry, in which the i ^ -operation changes sign of the scalar curvature, i ^ R = − R , and thus the Einstein–Hilbert action violates the i ^ -symmetry. In the alternative scenario of symmetry breaking, the gravitational coupling K = 1 / 16 π G plays the role of the order parameter, which changes sign under i ^ -transformation. [ABSTRACT FROM AUTHOR]

We investigate the benefits of future quantum accelerometers based on cold atom interferometry (CAI) on current and upcoming satellite gravity mission concepts. These mission concepts include satellite‐to‐satellite tracking (SST) in a single‐pair (GRACE‐like) and double‐pair constellation as well as satellite gravity gradiometry (SGG, single satellite, GOCE‐like). Regarding instruments, four scenarios are considered: current‐generation electrostatic (GRACE‐, GOCE‐like), next‐generation electrostatic, conservative hybrid/CAI and optimistic hybrid/CAI. For SST, it is shown that temporal aliasing poses currently the dominating error source in simulated global gravity field solutions independent of the investigated instrument and constellation. To still quantify the advantages of CAI instruments on the gravity functional itself, additional simulations are performed where the impact of temporal aliasing is synthetically reduced. When neglecting temporal aliasing, future accelerometers in conjunction with future ranging instruments can substantially improve the retrieval performance of the Earth's gravity field (depending on instrument and constellation). These simulation results are further investigated regarding possible benefit for hydrological use cases where these improvements can also be observed (when omitting temporal aliasing). For SGG, it is demonstrated that, with realistic instrument assumptions, one is still mostly insensitive to time‐variable gravity and not competitive with the SST principle. However, due to the improved instrument sensitivity of quantum gradiometers compared to the GOCE mission, static gravity field solutions can be improved significantly. Key Points: Quantum instruments may significantly improve the sensitivity of gravity measurementsA higher sensitivity cannot substantially improve current and upcoming satellite gravity missions due to temporal aliasing [ABSTRACT FROM AUTHOR]

Random tensor models have applications in a variety of fields, such as quantum gravity, quantum information theory, mathematics of modern technologies, etc. and studying their statistical properties, e.g. tensor eigenvalue/vector distributions, is interesting and useful. Recently some tensor eigenvalue/vector distributions have been computed by expressing them as partition functions of 0D quantum field theories. In this paper, using this method, we compute three cases of complex eigenvalue/vector distributions of symmetric order-three random tensors, where the three cases can be characterized by the Lie-group invariances, |$O(N,\mathbb {R})$|⁠ , |$O(N,\mathbb {C})$|⁠ , and |$U(N,\mathbb {C})$|⁠ , respectively. Exact closed-form expressions of the distributions are obtained by computing partition functions of four-fermi theories, where the last case is of the "signed" distribution, which counts the distribution with a sign factor coming from a Hessian matrix. As an application, we compute the injective norm of the complex symmetric order-three random tensor in the large- N limit by computing the edge of the last signed distribution, obtaining agreement with an earlier numerical result in the literature. [ABSTRACT FROM AUTHOR]

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 10 104 bits per second (bps). [ABSTRACT FROM AUTHOR]

We explicitly calculate the value of the cosmological constant, Λ , based on the recently developed theory connecting entropic gravity with quantum events induced by transactions, called transactional gravity. We suggest a novel interpretation of the cosmological constant and rigorously show its inverse proportionality to the squared radius of the causal universe Λ ~ R U − 2 . [ABSTRACT FROM AUTHOR]

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).