Quantum Gravity Models Research Articles

Fractional cosmic strings

Topological defects are investigated in the framework of quantum gravity models based on the hypothesis of an effective fractal dimension of the Universe. From a minimal coupling procedure, the tools of fractional calculus are used to determine the geometry associated to a fractional cosmic string. Several results for the propagation of light are discussed, notably the light-deviation angle due to the defect and the geodesics of light.

Analyzing quantum gravity spillover in the semiclassical regime

One of the standard approaches of incorporating the quantum gravity (QG) effects into the semiclassical analysis is to adopt the notion of a quantum-corrected spacetime arising from the QG model. This procedure assumes that the expectation value of the metric variable effectively captures the relevant QG subtleties in the semiclassical regime. We investigate the viability of this effective geometry approach for the case of dust dominated and a dark energy dominated universe. We write the phase space expressions for the geometric observables and construct corresponding Hermitian operators. A general class of operator ordering of these observables is considered, and their expectation values are calculated for a unitarily evolving wave packet. In the case of dust dominated universe, the expectation value of the Hubble parameter matches the “semiclassical” expression, the expression computed from the scale factor expectation value. In the case of the Ricci scalar, the relative difference between the semiclassical expression and quantum expectation is maximum at singularity and decays for late time. For a cosmological constant driven universe, the difference between the semiclassical expressions and the expectation value is most pronounced far away from the bounce point, hinting at the persistent quantum effect at the late time. The parameter related to the shape of the distribution appears as a control parameter in these models. In the limit of a sharply peaked distribution, the expectation value of the observables matches with their semiclassical counterpart, and the usage of effective geometry approach is justified.

Quantum gravity through geometric algebra

Geometric Algebra is used to construct a model of quantum gravity in which the 4D spacetime manifold is built from qubitic quantum entangled spacetime elements of geometric algebraic nature. This is achieved by first investigating the spontaneous decomposition of the spacetime continuum’s metric structure at Planck distances as one approaches what otherwise would become the Universe’s initial singularity. Considering this metric deconstruction within the model one finds that the reverse induced emergence of the spacetime continuum is generated by a coupling action triggered by the embedding action between distinct pre-spacetime manifolds. Further uncovered in this re-engineering of spacetime is a Poincaré-constrained quantum foam existing at infra-Planck scales.

Higher category theory and n-groups as gauge symmetries for quantum gravity

Higher category theory can be employed to generalize the notion of a gauge group to the notion of a gauge n-group. This novel algebraic structure is designed to generalize notions of connection, parallel transport and holonomy from curves to manifolds of dimension higher than one. Thus it generalizes the concept of gauge symmetry, giving rise to a topological action called nBF action, living on a corresponding n-principal bundle over a spacetime manifold. Similarly as for the Plebanski action, one can deform the topological nBF action by adding appropriate simplicity constraints, in order to describe the correct dynamics of both gravity and matter fields. Specifically, one can describe the whole Standard Model coupled to gravity as a constrained 3BF or 4BF action. The split of the full action into a topological sector and simplicity constraints sector is adapted to the spinfoam quantization technique, with the aim to construct a full model of quantum gravity with matter. In addition, the properties of the gauge n-group structure open up a possibility of a nontrivial unification of all fields. An n-group naturally contains additional novel gauge groups which specify the spectrum of matter fields present in the theory, in a similar way to the ordinary gauge group that prescribes the spectrum of gauge vector bosons in the Yang-Mills theory. The presence and the properties of these new gauge groups has the potential to explain fermion families, and other structure in the matter spectrum of the theory.

Towards Quantum Gravity in the Lab on Quantum Processors

The holographic principle and its realization in the AdS/CFT correspondence led to unexpected connections between general relativity and quantum information. This set the stage for studying aspects of quantum gravity models, which are otherwise difficult to access, in table-top quantum-computational experiments. Recent works have designed a special teleportation protocol that realizes a surprising communication phenomenon most naturally explained by the physics of a traversable wormhole. In this work, we have carried out quantum experiments based on this protocol on state-of-the-art quantum computers. The target quantum processing units (QPUs) included the Quantinuum's trapped-ion System Model H1-1 and five IBM superconducting QPUs of various architectures, with public and premium user access. We report the observed teleportation signals from these QPUs with the best one reaching 80% of theoretical predictions. We outline the experimental challenges we have faced in the course of implementation, as well as the new theoretical insights into quantum dynamics the work has led to. We also developed QGLab – an open-source end-to-end software solution that facilitates conducting the wormhole-inspired teleportation experiments on state-of-the-art and emergent generations of QPUs supported by the Qiskit and tket SDKs. We consider our study and deliverables as an early practical step towards the realization of more complex experiments for the indirect probing of quantum gravity in the lab.

Speed limits and locality in many-body quantum dynamics.

We review the mathematical speed limits on quantum information processing in many-body systems. After the proof of the Lieb-Robinson Theorem in 1972, the past two decades have seen substantial developments in its application to other questions, such as the simulatability of quantum systems on classical or quantum computers, the generation of entanglement, and even the properties of ground states of gapped systems. Moreover, Lieb-Robinson bounds have been extended in non-trivial ways, to demonstrate speed limits in systems with power-law interactions or interacting bosons, and even to prove notions of locality that arise in cartoon models for quantum gravity with all-to-all interactions. We overview the progress which has occurred, highlight the most promising results and techniques, and discuss some central outstanding questions which remain open. To help bring newcomers to the field up to speed, we provide self-contained proofs of the field's most essential results.

Phenomenological footprints of Λ varying gravity theories inspired from quantum gravity models in the multi-messenger era

An interesting phenomenological consequence of Λ varying gravity theories inspired by quantum gravity models is reported. The treatment in the present work is quite general and applicable to several different actions with Λ varying, especially those used in RG approaches to quantum gravity. An effective gravitational action with a scale varying cosmological constant, Λ, which depends on the system’s characteristics, like the length and the energy density, is the key feature. If the system is an astrophysical object, like a cluster of galaxies, a black hole, etc, non-negligible corrections arise to several observable quantities. Distinctive footprints could refer to luminosity distance and strong/weak lensing measurements, among others. The present study focuses on the SNIa luminosity distance observable.

Bouncing Universe in loop quantum gravity: full theory calculation

In loop quantum gravity mathematically rigorous models of full quantum gravity were proposed. In this paper we will study a cosmological sector of one of the models describing quantum gravity with positive cosmological constant coupled to massless scalar field. In our previous research we introduced a method to reduce the model to homogeneous-isotropic sector at the quantum level. In this paper we propose a method to restrict our homogeneous-isotropic model to the spatially flat sector. After this restriction the number of degrees of freedom gets substantially reduced. This allows us to make numerical and analytical calculations. Remarkably, the resulting model shares some structural similarities with the loop quantum cosmological models and therefore sheds some new light on the relation between loop quantum gravity and loop quantum cosmology. According to our model the evolution of the Universe is periodic. The quantum gravity effects resolve the Big Bang singularity leading to a Big Bounce and cause the Universe to contract after a classical expansion phase.

Critical JT gravity

In this paper, we investigate a critical behavior of JT gravity, a model of two-dimensional quantum gravity on constant negatively curved spacetimes. Our approach involves using techniques from random maps to investigate the generating function of Weil-Petersson volumes, which count random hyperbolic surfaces with defects. The defects are weighted geodesic boundaries, and criticality is reached by tuning the weights to the regime where macroscopic holes emerge in the hyperbolic surface, namely non-generic criticality. We analyze the impact of this critical regime on some universal features, such as its density of states. We present a family of models that interpolates between systems with ρ0(E) ~ sqrt{E-{E}_0} and ρ0(E) ~ (E − E0)3/2, which are commonly found in models of JT gravity coupled to dynamical end-of-the-world and FZZT branes, and give a precise definition of what this phase transition means from the random geometry point of view.

Massless graviton in a model of quantum gravity with emergent spacetime

Massless graviton in a model of quantum gravity with emergent spacetime

First Experimental Survey of a Whole Class of Non-Commutative Quantum Gravity Models in the VIP-2 Lead Underground Experiment

This study is aimed to set severe constraints on a whole class of non-commutative space-times scenarios as a class of universality for several quantum gravity models. To this end, slight violations of the Pauli exclusion principle—predicted by these models—are investigated by searching for Pauli forbidden Kα and Kβ transitions in lead. The selection of a high atomic number target material allows to test the energy scale of the space-time non-commutativity emergence at high atomic transition energies. As a consequence, the measurement is very sensitive to high orders in the power series expansion of the Pauli violation probability, which allows to set the first constraint to the “triply special relativity” model proposed by Kowalski-Glikman and Smolin. The characteristic energy scale of the model is bound to Λ>5.6·10−9 Planck scales.

Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model

We consider transition amplitudes in the coloured simplicial Boulatov model for three-dimensional Riemannian quantum gravity. First, we discuss aspects of the topology of coloured graphs with non-empty boundaries. Using a modification of the standard rooting procedure of coloured tensor models, we then write transition amplitudes systematically as topological expansions. We analyse the transition amplitudes for the simplest boundary topology, the 2-sphere, and prove that they factorize into a sum entirely given by the combinatorics of the boundary spin network state and that the leading order is given by graphs representing the closed 3-ball in the large N limit. This is the first step towards a more detailed study of the holographic nature of coloured Boulatov-type GFT models for topological field theories and quantum gravity.

Cellular automaton for spinor gravity in four dimensions

Certain fermionic quantum field theories are equivalent to probabilistic cellular automata, with fermionic occupation numbers associated to bits. We construct an automaton that represents a discrete model of spinor gravity in four dimensions. Local Lorentz symmetry is exact on the discrete level and diffeomorphism symmetry emerges in the naive continuum limit. Our setting could serve as a model for quantum gravity if diffeomorphism symmetry is realized in the true continuum limit and suitable collective fields for vierbein and metric acquire non-vanishing expectation values. The discussion of this interesting specific model reveals may key qualitative features of the continuum limit for probabilistic cellular automata. This limit obtains for a very large number of cells if the probabilistic information is sufficiently smooth. It is associated to coarse graining. The automaton property that every bit configuration is updated at every discrete time step to precisely one new bit configuration does no longer hold on the coarse grained level. A coarse grained configuration of occupation numbers can evolve into many different configurations with certain probabilities. This characteristic feature of quantum field theories can come along with the emergence of continuous space-time symmetries.

Beyond semiclassical time: dynamics in quantum cosmology

We review two approaches to the definition of the Hilbert space and evolution in mechanical theories with local time-reparametrization invariance, which are often used as toy models of quantum gravity. The first approach is based on the definition of invariant relational observables, whereas the second formalism consists of a perturbative construction of the Hilbert space and a weak-coupling expansion of the Hamiltonian constraint, which is frequently performed as part of the Born-Oppenheimer treatment in quantum cosmology. We discuss in which sense both approaches exhibit an inner product that is gauge-fixed via an operator version of the usual Faddeev-Popov procedure, and, in the second approach, how the unitarity of the effective Schrödinger evolution is established perturbatively. We note that a conditional probability interpretation of the physical states is possible, so that both formalisms are examples of quantum mechanics with a relational dynamics.

Discriminating quantum gravity models by gravitational decoherence

Several phenomenological approaches to quantum gravity predict the existence of a minimal measurable length and/or a maximum measurable momentum near the Planck scale. When embedded into the framework of quantum mechanics, such constraints induce a modification of the canonical commutation relations and thus a generalization of the Heisenberg uncertainty relations, commonly referred to as generalized uncertainty principle (GUP). Different models of quantum gravity imply different forms of the GUP. For instance, in the framework of string theory the GUP is quadratic in the momentum operator, while in the context of doubly special relativity it includes an additional linear dependence. Among the possible physical consequences, it was recently shown that the quadratic GUP induces a universal decoherence mechanism, provided one assumes a foamy structure of quantum spacetime close to the Planck length. Along this line, in the present work we investigate the gravitational decoherence associated to the linear-quadratic GUP and we compare it with the one associated to the quadratic GUP. We find that, despite their similarities, the two generalizations of the Heisenberg uncertainty principle yield decoherence times that are completely uncorrelated and significantly distinct. Motivated by this result, we introduce a theoretical and experimental scheme based on cavity optomechanics to measure the different time evolution of nonlocal quantum correlations corresponding to the two aforementioned decoherence mechanisms. We find that the deviation between the two predictions occurs on time scales that are macroscopic and thus potentially amenable to experimental verification. This scenario provides a possible setting to discriminate between different forms of the GUP and therefore different models of quantum gravity.

Neutrino decoherence from generalised uncertainty

Quantum gravity models predict a minimal measurable length which gives rise to a modification in the uncertainty principle. One of the simplest manifestations of these generalised uncertainty principles is the linear quadratic generalised uncertainty principle which leads to a modified Heisenberg algebra. This can alter the usual von-Neumann evolution of density matrix to a Lindblad-type equation. We show how this can give rise to a decoherence in neutrino propagation in vacuum. The decoherence effects due to the linear quadratic generalised uncertainty principle are extremely minimal and is unlikely to be detectable in the existing or upcoming experimental facilities for any of the natural sources of neutrinos. We also show that, in principle, there can be other variants of generalised uncertainty principle which predicts verifiable decoherence effects for the cosmic neutrino background.

Generalised spectral dimensions in non-perturbative quantum gravity

The seemingly universal phenomenon of scale-dependent effective dimensions in non-perturbative theories of quantum gravity has been shown to be a potential source of quantum gravity phenomenology. The scale-dependent effective dimension from quantum gravity has only been considered for scalar fields. It is, however, possible that the non-manifold like structures, that are expected to appear near the Planck scale, have an effective dimension that depends on the type of field under consideration. To investigate this question, we have studied the spectral dimension associated to the Laplace–Beltrami operator generalised to k-form fields on spatial slices of the non-perturbative model of quantum gravity known as causal dynamical triangulations. We have found that the two-form, tensor and dual scalar spectral dimensions exhibit a flow between two scales at which an effective dimension appears. However, the one-form and vector spectral dimensions show only a single effective dimension. The fact that the one-form and vector spectral dimension do not show a flow of the effective dimension can potentially be related to the absence of a dispersion relation for the electromagnetic field, but dynamically generated instead of as an assumption.

Generalized Heisenberg Uncertainty Principle due to the quantum gravitational effects in the Schwarzschild spacetime

In non-relativistic quantum mechanics, the Heisenberg Uncertainty Principle states a fundamental limit to the accuracy in the measurement of pairs of conjugate variables, such as position and momentum. Based on a semiclassical geometric approach, it has been recently proposed a generalization of the uncertainty principle under the relativistic case, which could be extended to General Relativity. This formalism was applied to the Schwarzschild and de Sitter spacetime, showing that the uncertainty relations obtained can be mapped into deformations of Generalized Heisenberg principles well-known in the literature and obtained from the different models of quantum gravity proposed. In the present study, the generalized Heisenberg Principle is derived from the commutator relation, and has been applied to the classical gravitational tests and the derived consequences are framed and analyzed.

Euclidean dynamical triangulations revisited

We conduct numerical simulations of a model of four-dimensional quantum gravity in which the path integral over continuum Euclidean metrics is approximated by a sum over combinatorial triangulations. At fixed volume, the model contains a discrete Einstein-Hilbert term with coupling $\ensuremath{\kappa}$ and a local measure term with coupling $\ensuremath{\beta}$ that weights triangulations according to the number of simplices sharing each vertex. We map out the phase diagram in this two-dimensional parameter space and compute a variety of observables that yield information on the nature of any continuum limit. Our results are consistent with a line of first-order phase transitions with a latent heat that decreases as $\ensuremath{\kappa}\ensuremath{\rightarrow}\ensuremath{\infty}$. We find a Hausdorff dimension along the critical line that approaches ${D}_{H}=4$ for large $\ensuremath{\kappa}$ and a spectral dimension consistent with ${D}_{s}=\frac{3}{2}$ at short distances. These results are broadly in agreement with earlier works on Euclidean dynamical triangulation models which utilize degenerate triangulations and/or different measure terms and indicate that such models exhibit a degree of universality.

Thermodynamics of Schwarzschild black hole surrounded by quintessence in gravity's rainbow

According to some quantum gravity models, Lorentz invariance can be violated in the Planck energy scale. With this motivation, we analyze the thermal quantities and the stability of Schwarzschild black hole surrounded by quintessence in gravity's rainbow formalism. To do that, we consider the rainbow functions which are motivated by loop quantum gravity and gamma-ray bursts, and we derive Hawking temperature, specific heat, entropy and the equation of state function. We observe that the presence the quintessence matter field and rainbow gravity affect the stability of the black hole.