Quantum Gravity Models Research Articles

Fractional quantum mechanics meets quantum gravity phenomenology

Abstract This letter extends previous findings on the modified Schrödinger evolution inspired by quantum gravity phenomenology. By establishing a connection between this approach and fractional quantum mechanics, we provide insights into a potential deep infrared regime of quantum gravity, characterized by the emergence of fractal dimensions, similar to behaviors observed in the deep ultraviolet regime. Additionally, we explore the experimental investigations of this regime using Bose-Einstein condensates. Notably, our analysis reveals a direct implication of this analogy: general experiments probing fractional quantum mechanics may serve as equivalent models of quantum gravity. We identify instances of nonlocal behavior in such systems, suggesting an analogous phenomenon of nonlocality in quantum gravity.

Quasinormal modes of slowly-spinning horizonless compact objects

One of the main predictions of general relativity is the existence of black holes featuring a horizon beyond which nothing can escape. Gravitational waves from the remnants of compact binary coalescences have the potential to probe new physics close to the black hole horizons. This prospect is of particular interest given several quantum-gravity models that predict the presence of horizonless and singularity-free compact objects. The membrane paradigm is a generic framework that allows one to parametrize the interior of compact objects in terms of the properties of a fictitious fluid located at the object’s radius. It has been used to derive the quasinormal mode spectrum of static horizonless compact objects. Extending the membrane paradigm to rotating objects is crucial to constrain the properties of the spinning merger remnants. In this work, we extend the membrane paradigm to linear order in spin and use it to analyze the relationships between the quasinormal modes, the object’s reflectivity, and the membrane parameters. We find a breaking of isospectrality between axial and polar modes when the object is partially reflecting or the compactness differs from the black hole case. We also find that in reflective ultracompact objects some of the modes tend toward instability as the spin increases. Finally, we show that the spin enhances the deviations from the black-hole quasinormal mode spectrum as the compactness decreases. This implies that spinning horizonless compact objects may be more easily differentiated than nonspinning ones in the prompt ringdown. Published by the American Physical Society 2024

Decoding Quantum Gravity Information with Black Hole Accretion Disk

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.

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.

Gravitational-wave background in bouncing models from semi-classical, quantum and string gravity

We study the primordial spectra and the gravitational-wave background (GWB) of three models of semi-classical, quantum or string gravity where the big bang is replaced by a bounce and the primordial tensor spectrum is blue: ekpyrotic universe with fast-rolling Galileons, string-gas cosmology with Atick-Witten conjecture and pre-big-bang cosmology. We find that the ekpyrotic scenario with Galileons does not produce a GWB amplitude detectable by present or third-generation interferometers, while the Atick-Witten-based string-gas model is ruled out in its present form for violating the big-bang-nucleosynthesis bound, contrary to the original string-gas scenario. In contrast, the GWB of the pre-big-bang scenario falls within the sensitivity window of both LISA and Einstein Telescope, where it takes the form of a single or a broken power law depending on the choice of parameters. The latter will be tightly constrained by both detectors.

Generalized entanglement capacity of de Sitter space

Near horizons, quantum fields of low spin exhibit densities of states that behave asymptotically like 1+1 dimensional conformal field theories. In effective field theory, imposing some short-distance cutoff, one can compute thermodynamic quantities associated with the horizon, and the leading cutoff sensitivity of the heat capacity is found to equal to the leading cutoff sensitivity of the entropy. One can also compute contributions to the thermodynamic quantities from the gravitational path integral. For the cosmological horizon of the static patch of de Sitter space, a natural conjecture for the relevant heat capacity is shown to equal the Bekenstein-Hawking entropy. These observations allow us to extend the well-known notion of the generalized entropy to a generalized heat capacity for the static patch of de Sitter (dS). The finiteness of the entropy and the nonvanishing of the generalized heat capacity suggest it is useful to think about dS as a state in a finite dimensional quantum gravity model that is not maximally uncertain. Published by the American Physical Society 2024

Correction to the quantum relation of photons in the Doppler effect based on a special Lorentz violation model

The possibility of the breaking of Lorentz symmetry has been discussed in many models of quantum gravity. In this paper we follow the Lorentz violation model in Ref. [14] (i.e., our previous work) to discuss the Doppler frequency shift of photons and the Compton scattering process between photons and electrons, pointing out that following the idea in Ref. [14] we have to modify the usual quantum relation of photons in the Doppler effect. But due to the current limited information and knowledge, we could not yet determine the specific expression for the correction coefficient in the modified quantum relation of photons. However, the phenomenon called spontaneous radiation in a cyclotron maser give us an opportunity to see what the expression for this correction coefficient might look like. Therefor, under some necessary constraints, we construct a very concise expression for this correction coefficient through the discussion of different cases. And then we use this expression to analyze the wavelength of radiation in the cyclotron maser, which tends to a limited value at v → c, rather than to 0 as predicted by the Lorentz model. And the inverse Compton scattering phenomenon is also discussed and we find that there is a limit to the maximum energy that can be obtained by photons in the collision between extremely relativistic particles and low-energy photons, which conclusion is also very different from that obtained from the Lorentz model, in which the energy that can be obtained by the photon tends to be infinite as the velocity of particle is close to c. This paper still follows the purpose in Ref. [14] that the energy and momentum of particles (i.e., any particles, including photons) cannot be infinite, otherwise it will make some physical scenarios invalid. When the parameter Q characterizing the degree of deviation from the Lorentz model is equal to 0, all the results and conclusions in this paper will return to the case as in the Lorentz model, so this paper also provides us with a possible experimental scheme to determine the value of Q in Ref. [14], although it still requires extremely high experimental energy.

Approximate Quantum Codes From Long Wormholes

We discuss families of approximate quantum error correcting codes which arise as the nearly-degenerate ground states of certain quantum many-body Hamiltonians composed of non-commuting terms. For exact codes, the conditions for error correction can be formulated in terms of the vanishing of a two-sided mutual information in a low-temperature thermofield double state. We consider a notion of distance for approximate codes obtained by demanding that this mutual information instead be small, and we evaluate this mutual information for the SYK model and for a family of low-rank SYK models. After an extrapolation to nearly zero temperature, we find that both kinds of models produce fermionic codes with constant rate as the number, N, of fermions goes to infinity. For SYK, the distance scales as N1/2, and for low-rank SYK, the distance can be arbitrarily close to linear scaling, e.g. N.99, while maintaining a constant rate. We also consider an analog of the no low-energy trivial states property which we dub the no low-energy adiabatically accessible states property and show that these models do have low-energy states that can be prepared adiabatically in a time that does not scale with system size N. We discuss a holographic model of these codes in which the large code distance is a consequence of the emergence of a long wormhole geometry in a simple model of quantum gravity.

Energy flow of λ in Hořava-Lifshitz cosmology

Hořava-Lifshitz gravity has been proposed as a renormalizable and ghost-free quantum gravity model candidate with an anisotropic UV-scaling between space and time. We present here a cosmological background analysis of two different formulations of the theory, with particular focus on the running of the parameter λ. Using a large dataset consisting of cosmic microwave background data from , Pantheon+supernovae catalog, SH0ES Cepheid variable stars, baryon acoustic oscillations (BAO), cosmic chronometers, and gamma-ray bursts (GRB), we arrive at new bounds on the cosmological parameters, in particular λ, which runs logarithmically with energy and describes deviation from general relativity, which corresponds to λ=1 For the detailed balance scenario we arrive at the bound λ=1.0406±0.0023, and for beyond detailed balance the limit reads λ=1.0064±0.0002. We also study the influence of different datasets and priors, and we find that removing low-redshift data generally moves λ closer toward UV values, while simultaneously widening the error bars. In the detailed balance scenario, this effect is more noticeable, and without prior λ≥1 it takes on values that are significantly below unity. Published by the American Physical Society 2024

The semi-classical saddles in three-dimensional gravity via holography and mini-superspace approach

We determine the complex geometries dual to the semi-classical saddles in three-dimensional gravity with positive or negative cosmological constant. We examine the semi-classical saddles in Liouville field theory and interpret them in terms of gravity theory. For this, we describe the gravity theory by Chern-Simons theory and classify the possible saddles based on the homotopy group argument. We further realize the semi-classical saddles using the mini-superspace model of quantum gravity and explicitly determine the integral contour. In the case of positive cosmological constant, we recovered the geometry used for no-boundary proposal of Hartle and Hawking. In the case of negative cosmological constant, the geometry can be identified with Euclidean anti-de Sitter space attached with imaginary radius spheres. The geometry should be unphysical and several arguments on this issue are provided. Partial results were already presented in our earlier letter, and more detailed derivations and explanations on the results are given along with additional results. In particular, we reproduce the classical Liouville action from the Chern-Simons formulation of dual gravity theory.

Irreversible vierbein postulate: Emergence of spacetime from quantum phase transition

We formulate a model for quantum gravity based on the local Lorentz symmetry and general-coordinate invariance. A key idea is the irreversible vierbein postulate that a tree-level action for the model at a certain energy scale does not contain an inverse vierbein. Under this postulate, only the spinor becomes a dynamical field, and no gravitational background field is introduced in the tree-level action. In this paper, after explaining the transformation rules of the local Lorentz and general-coordinate transformations in detail, a tree-level action is defined. We show that fermionic fluctuations can induce a nonvanishing gravitational background field. Published by the American Physical Society 2024

Coloured combinatorial maps and quartic bi-tracial 2-matrix ensembles from noncommutative geometry

We compute the first twenty moments of three convergent quartic bi-tracial 2-matrix ensembles in the large N limit. These ensembles are toy models for Euclidean quantum gravity originally proposed by John Barrett and collaborators. A perturbative solution is found for the first twenty moments using the Schwinger-Dyson equations and properties of certain bi-colored unstable maps associated to the model. We then apply a result of Guionnet et al. to show that the perturbative and convergent solution coincide for a small neighbourhood of the coupling constants. For each model we compute an explicit expression for the free energy, critical points, and critical exponents in the large N limit. In particular, the string susceptibility is found to be γ = 1/2, hinting that the associated universality class of the model is the continuous random tree.

Simulating electromagnetic cascades with Lorentz invariance violation

Lorentz invariance violation (LIV) is a phenomenon featuring in various quantum gravity models whereby Lorentz symmetry is broken at high energies, potentially impacting the behaviour of particles and their interactions. Here we investigate the phenomenology of LIV within the context of gamma-ray–induced electromagnetic cascades. We conduct detailed numerical simulations to explore the expected manifestations of LIV on gamma-ray fluxes, taking into account relevant effects such as pair production and inverse Compton scattering. Additionally, we consider processes forbidden in the standard model, namely vacuum Cherenkov emission and photon decay. Our analysis reveals that these modifications result in distinct characteristics within the measured particle fluxes at Earth, which have the potential to be observed in high-energy gamma-ray observations.

Information scrambling —A quantum thermodynamic perspective

Recent advances in quantum information science have shed light on the intricate dynamics of quantum many-body systems, for which quantum information scrambling is a perfect example. Motivated by considerations of the thermodynamics of quantum information, this perspective aims at synthesizing key findings from several pivotal studies and exploring various aspects of quantum scrambling. We consider quantifiers such as the out-of-time-ordered correlator (OTOC) and the quantum mutual information, their connections to thermodynamics, and their role in understanding chaotic vs. integrable quantum systems. With a focus on representative examples, we cover a range of topics, including the thermodynamics of quantum information scrambling, and the scrambling dynamics in quantum gravity models such as the Sachdev-Ye-Kitaev (SYK) model. Examining these diverse approaches enables us to highlight the multifaceted nature of quantum information scrambling and its significance in understanding the fundamental aspects of quantum many-body dynamics at the intersection of quantum mechanics and thermodynamics.

Inequivalence of mimetic gravity with models of loop quantum gravity

Inequivalence of mimetic gravity with models of loop quantum gravity

Causal Structure in Spin Foams

The metric field of general relativity is almost fully determined by its causal structure. Yet, in spin foam models of quantum gravity, the role played by the causal structure is still largely unexplored. The goal of this paper is to clarify how causality is encoded in such models. The quest unveils the physical meaning of the orientation of the two-complex and its role as a dynamical variable. We propose a causal version of the EPRL spin foam model and discuss the role of the causal structure in the reconstruction of a semiclassical space–time geometry.

A High-Finesse Suspended Interferometric Sensor for Macroscopic Quantum Mechanics with Femtometre Sensitivity.

We present an interferometric sensor for investigating macroscopic quantum mechanics on a table-top scale. The sensor consists of a pair of suspended optical cavities with finesse over 350,000 comprising 10 g fused silica mirrors. The interferometer is suspended by a four-stage, light, in-vacuum suspension with three common stages, which allows for us to suppress common-mode motion at low frequency. The seismic noise is further suppressed by an active isolation scheme, which reduces the input motion to the suspension point by up to an order of magnitude starting from 0.7 Hz. In the current room-temperature operation, we achieve a peak sensitivity of 0.5 fm/Hz in the acoustic frequency band, limited by a combination of readout noise and suspension thermal noise. Additional improvements of the readout electronics and suspension parameters will enable us to reach the quantum radiation pressure noise. Such a sensor can eventually be utilized for demonstrating macroscopic entanglement and for testing semi-classical and quantum gravity models.

Emergent modified gravity

A complete canonical formulation of general covariance makes it possible to construct new modified theories of gravity that are not of higher-curvature form, as shown here in a spherically symmetric setting. The usual uniqueness theorems are evaded by using a crucial and novel ingredient, allowing for fundamental fields of gravity distinct from an emergent space-time metric that provides a geometrical structure to all solutions. As specific examples, there are new expansion-shear couplings in cosmological models, a form of modified Newtonian dynamics can appear in a space-time covariant theory without introducing extra fields, and related effects help to make effective models of canonical quantum gravity fully consistent with general covariance.

Random finite noncommutative geometries and topological recursion

In this paper, we investigate a model for quantum gravity on finite noncommutative spaces using the theory of blobbed topological recursion. The model is based on a particular class of random finite real spectral triples {(\mathcal{A}, \mathcal{H}, D, \gamma, J)} , called random matrix geometries of type {(1,0)} , with a fixed fermion space {(\mathcal{A}, \mathcal{H}, \gamma, J)} and a distribution of the form {e^{- \mathcal{S} (D)}\, {\mathrm{d}} D} over the moduli space of Dirac operators. The action functional {\mathcal{S} (D)} is considered to be a sum of terms of the form {\prod_{i=1}^s \mathrm{Tr} ({D^{n_i}})} for arbitrary {s \geqslant 1} . The Schwinger–Dyson equations satisfied by the connected correlators {W_n} of the corresponding multi-trace formal 1-Hermitian matrix model are derived by a differential geometric approach. It is shown that the coefficients {W_{g,n}} of the large N expansion of {W_n} ’s enumerate discrete surfaces, called stuffed maps, whose building blocks are of particular topologies. The spectral curve {( {\Sigma, \omega_{0,1}, \omega_{0,2}} )} of the model is investigated in detail. In particular, we derive an explicit expression for the fundamental symmetric bidifferential {\omega_{0,2}} in terms of the formal parameters of the model.

Pregeometric Spaces from Wolfram Model Rewriting Systems as Homotopy Types

How do spaces in physics emerge from pregeometric discrete building blocks governed by computational rules? To address this question we investigate non-deterministic rewriting systems (so-called multiway systems) of the Wolfram model. We express these rewriting systems as homotopy types. Using this new formulation of the model, we motivate how spatial structures are functorially inherited from pregeometric type-theoretic constructions. We show how higher homotopies are constructed from rewriting rules. These correspond to morphisms of an n-fold category. Subsequently, the n→∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n \\rightarrow \\infty $$\\end{document} limit of the Wolfram model rulial multiway system is identified as an ∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\infty $$\\end{document}-groupoid, with the latter being relevant in light of Grothendieck’s homotopy hypothesis. We then go on to show how this construction extends to the classifying space of rulial multiway systems, which forms a multiverse of multiway systems and carries the formal structure of an ∞,1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\left( \\infty , 1\\right) }$$\\end{document}-topos. This correspondence to higher categorical structures potentially offers a new way to understand how the kinds of spaces relevant to physics result from pregeometric combinatorial models. The key issue we have addressed in this work is to relate abstract non-deterministic rewriting systems to higher homotopy spaces. A consequence of constructing spaces and geometry synthetically is that it removes the need to make ad hoc assumptions about geometric attributes of a model such as an a priori background or any pre-assigned geometric data. Instead, geometry is inherited functorially from higher structures. This can be particularly useful for formally justifying different choices of underlying spacetime discretization schemes adopted by various models of quantum gravity. We conclude with comments on how our framework of higher category-theoretic combinatorial constructions closely corroborates with other approaches investigating higher categorical structures relevant to the foundations of physics.