Quantum Gravity Phenomenology Research Articles

Fractional quantum mechanics meets quantum gravity phenomenology

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.

Quantum gravity phenomenology and the blackbody radiation

Abstract We analyze the blackbody radiation problem in the presence of quantum gravity effects encoded in modified dispersion relations. The spectral radiance and the generalized Stefan-Boltzmann law are studied in this context. Furthermore, the regime of low temperatures is also contemplated, where features related to the blackbody thermal laws and the thermodynamic quantities such as energy, pressure, entropy, and specific heat are obtained. Possible implications in compact objects such as neutron stars are also discussed.

Planck Length Emerging as the Invariant Quantum Minimum Effective Length Determined by the Heisenberg Uncertainty Principle in Manifestly Covariant Quantum Gravity Theory

The meaning of the quantum minimum effective length that should distinguish the quantum nature of a gravitational field is investigated in the context of manifestly covariant quantum gravity theory (CQG-theory). In such a framework, the possible occurrence of a non-vanishing minimum length requires one to identify it necessarily with a 4-scalar proper length s.It is shown that the latter must be treated in a statistical way and associated with a lower bound in the error measurement of distance, namely to be identified with a standard deviation. In this reference, the existence of a minimum length is proven based on a canonical form of Heisenberg inequality that is peculiar to CQG-theory in predicting massive quantum gravitons with finite path-length trajectories. As a notable outcome, it is found that, apart from a numerical factor of O1, the invariant minimum length is realized by the Planck length, which, therefore, arises as a constitutive element of quantum gravity phenomenology. This theoretical result permits one to establish the intrinsic minimum-length character of CQG-theory, which emerges consistently with manifest covariance as one of its foundational properties and is rooted both on the mathematical structure of canonical Hamiltonian quantization, as well as on the logic underlying the Heisenberg uncertainty principle.

Imprints of a gravitational wave through the weak field deflection of photons* *A. Ö. and R. P. acknowledge the networking support of the COST Action CA18108 - COST Action CA21106 - COSMIC WISPers in the Dark Universe: Theory, astrophysics and experiments (CosmicWISPers), Quantum gravity phenomenology in the multi-messenger approach (QG-MM), the COST Action CA21136 - Addressing observational tensions in cosmology

In this study, we investigate the novel phenomenon of gravitational lensing experienced by gravitational waves traveling past a Schwarzschild black hole perturbed by a specific, first-order, polar gravitational wave. We apply the Gauss-Bonnet theorem, finding a topological contribution to the deflection of light rays passing near the black hole. We demonstrate that the deflection angle can be determined by analyzing a region entirely outside the path of the light ray, leading to a calculation based solely on the parameters of the perturbing wave (Legendre polynomial order, l; frequency, σ). This approach offers a unique perspective on gravitational lensing and expands our understanding of black hole interactions with gravitational waves.

Towards quantum mechanics on the curved cotangent bundle

The minimal-length paradigm is a cornerstone of quantum gravity phenomenology. Recently, it has been demonstrated that minimal-length quantum mechanics can alternatively be described as an undeformed theory set on a nontrivial momentum space. However, there is no fully consistent formulation of these theories beyond Cartesian coordinates in flat space and, in particular, no position representation. This paper is intended to take the first steps in bridging this gap. We find a natural position representation of the position and momentum operators on general curved cotangent bundles. In an expansion akin to Riemann normal coordinates with curvature in both position and momentum space, we apply the formalism perturbatively to the isotropic harmonic oscillator and the hydrogenic atom. Due to the symmetry of the harmonic oscillator under exchange of positions and momenta, we show that it is impossible to distinguish position- from momentum-space curvature with oscillators alone. Thus, we obtain an instantiation of Born reciprocity on the curved cotangent bundle, i.e. in precisely the way Born originally envisioned. It manifests itself as a symmetry mixing UV and IR physics, reminiscent of T-duality in string theory.

Phenomenology of DSR-relativistic in-vacuo dispersion in FLRW spacetime

Studies of in-vacuo dispersion are the most active area of quantum-gravity phenomenology. The way in which in-vacuo dispersion produces redshift-dependent corrections to the time of flight of astrophysics particles depends on the model-dependent interplay between Planck-scale effects and spacetime curvature/expansion, and we here derive the most general formula for the leading order redshift-dependent correction to the time of flight for the scenario in which relativistic symmetries are deformed at the Planck scale (DSR) for the constant-curvature case. We find that, contrary to the broken symmetries scenario (LIV), where in principle any arbitrary form of redshift dependence could be allowed, for the DSR scenario only linear combinations of three possible forms of redshift dependence are allowed. We also derive a generalization of our results to the FRW case, and discuss some specific combinations of the three forms of redshift dependence whose investigation might deserve priority from the quantum-gravity perspective.

Kinetic gases in static spherically symmetric modified dispersion relations

We study the dynamics of a collisionless kinetic gas in the most general static, spherically symmetric dispersion relation. For a static, spherically symmetric kinetic gas, we derive the most general solution to these dynamics, and find that any solution is given by a one-particle distribution function which depends on three variables. For two particular solutions, describing a shell of monoenergetic orbiting particles and a purely radial inflow, we calculate the particle density as a function of the radial coordinate. As a particular example, we study a κ-Poincaré modification of the Schwarzschild metric dispersion relation and derive its influence on the particle density. Our results provide a possible route towards quantum gravity phenomenology via the observation of matter dynamics in the vicinity of massive compact objects.

Constraining Snyder and GUP models with low-mass stars

We investigate the application of an equation of state that incorporates corrections derived from the Snyder model (and the Generalized Uncertainty Principle) to describe the behaviour of matter in a low-mass star. Remarkably, the resulting equations exhibit striking similarities to those arising from modified Einstein gravity theories. By modeling matter with realistic considerations, we are able to more effectively constrain the theory parameters, surpassing the limitations of existing astrophysical bounds. The bound we obtain is β0≤4.5×1047\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _0 \\le 4.5 \ imes 10^{47}$$\\end{document}. We underline the significance of realistic matter modeling in order to enhance our understanding of effects arising in quantum gravity phenomenology and implications of quantum gravitational corrections in astrophysical systems.

Quantum gravity phenomenology from the perspective of quantum general relativity and quadratic gravity

Multi-messenger astronomy provides us with the possibility of discovering phenomenological signatures of quantum-gravity effects. This should be of paramount importance in the pursuit of an elusive quantum theory for the gravitational interactions. Here we discuss feasible explorations within the effective field theory (EFT) treatment of general relativity. By exploring current techniques borrowed from modern amplitude methods, we calculate leading quantum corrections to the classical radiated momentum and spectral waveforms. The lessons drawn from these low-energy results are that phenomenological applications in gravitational-wave physics can be discussed in line with the EFT approach. In turn, we also examine possible phenomenological surveys from the perspective of a UV completion for quantum gravity which employs the metric as the fundamental dynamical variable, namely quadratic gravity. Being more specific, by resorting to the eikonal approximation, we compute the leading-order time delay/advance in the scattering of light by a heavy object and find a possible significant deviation from the standard general-relativity prediction. This allows us to probe causal uncertainty due to quantum fluctuations of the gravitational field as a genuine prediction from Planck-scale physics.

On Efforts to Decouple Early Universe Cosmology and Quantum Gravity Phenomenology

On Efforts to Decouple Early Universe Cosmology and Quantum Gravity Phenomenology

Symmetries of κ-Minkowski space-time: a possibility of exotic momentum space geometry?

The quest for a quantum gravity phenomenology has inspired a quantum notion of space-time, which motivates us to study the fate of the relativistic symmetries of a particular model of quantum space-time, as well as its intimate connection with the plausible emergent curved “physical momentum space”. We here focus on the problem of Poincare symmetry of κ-Minkowski type non-commutative (quantum) space-time, where the Poincare algebra, on its own, remains undeformed, but in order to preserve the structure of the space-time non-commutative (NC) algebra, the actions of the algebra generators on the operator-valued space-time manifold must be enveloping algebra valued that lives in entire phase space i.e. the cotangent bundle on the space-time manifold (at classical level). Further, we constructed a model for a spin-less relativistic massive particle enjoying the deformed Poincare symmetry, using the first order form of geometric Lagrangian, that satisfies a new deformed dispersion relation and explored a feasible regime of a future Quantum Gravity theory in which the momentum space becomes curved. In this scenario there is only a mass scale (Planck mass mp), but no length scale. Finally, we relate the deformed mass shell to the geodesic distance in this curved momentum space, where the mass of the particle gets renormalized as a result of noncommutativity. We show, that under some circumstances, the Planck mass provides an upper bound for the observed renormalized mass.

Triple interference, non-linear Talbot effect and gravitization of the quantum

Recently we have discussed a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini–Study metric in the Hilbert space of states, become dynamical and so implement the idea of gravitizing the quantum. In this paper we elaborate on a specific test of this new approach to quantum gravity using triple interference in a varying gravitational field. Our discussion is driven by a profound analogy with recent triple-path interference experiments performed in the context of non-linear optics. We emphasize that the triple interference experiment in a varying gravitational field would deeply influence the present understanding of the kinematics of quantum gravity and quantum gravity phenomenology. We also discuss the non-linear Talbot effect as another striking phenomenological probe of gravitization of the geometry of quantum theory.

Momentum gauge fields from curved momentum space through Kaluza–Klein reduction

In this work we investigate the relation between curved momentum space and momentum-dependent gauge fields. While the former is a classic idea that has been shown to be tied to minimal-length models, the latter constitutes a relatively recent development in quantum gravity phenomenology. In particular, the gauge principle in momentum space amounts to a modification of the position operator of the form akin to a gauge-covariant derivative in momentum space according to the minimal coupling prescription. Here, we derive both effects from a Kaluza–Klein reduction of a higher-dimensional geometry exhibiting curvature in momentum space. The interplay of the emerging gauge fields as well as the remaining curved momentum space lead to modifications of the Heisenberg algebra. While the gauge fields imply Moyal-type noncommutativity dependent on the analogue field strength tensor, the dimensionally reduced curved momentum space geometry translates to a Snyder-type noncommutative geometry.

Finite temperature considerations in the structure of quadratic GUP-modified white dwarfs

In quantum gravity phenomenology, the effect of the generalized uncertainty principle (GUP) on white dwarf structure has been given much attention in recent literature. However, these studies assume a zero temperature equation of state (EoS), excluding young white dwarfs whose initial temperatures are substantially high. To that cause, this paper calculates the Chandrasekhar EoS and resulting mass-radius relations of finite temperature white dwarfs modified by the quadratic GUP, an approach that extends Heisenberg’s uncertainty principle by a quadratic term in momenta. The EoS was first approximated by treating the quadratic GUP parameter as perturbative, causing the EoS to exhibit expected thermal deviations at low pressures, and conflicting behaviors at high pressures, depending on the order of approximation. We then proceeded with a full numerical simulation of the modified EoS, and showed that in general, finite temperatures cause the EoS at low pressures to soften, while the quadratic GUP stiffens the EoS at high pressures. This modified EoS was then applied to the Tolman–Oppenheimer–Volkoff equations and its classical approximation to obtain the modified mass-radius relations for general relativistic and Newtonian white dwarfs. The relations for both cases were found to exhibit the expected thermal deviations at small masses, where low-mass white dwarfs are shifted to the high-mass regime at large radii, while high-mass white dwarfs acquire larger masses, beyond the Chandrasekhar limit. Additionally, we find that for sufficiently large values of the GUP parameter and temperature, we obtain mass-radius relations that are completely removed from the ideal case, as high-mass deviations due to GUP and low-mass deviations due to temperature are no longer mutually exclusive.

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.

Effect of generalized uncertainty principle on anharmonic oscillator

The minimal length Generalized Uncertainty Principle (GUP) is a proposed theory based on the basic phenomenology of Quantum Gravity (QG) to study the effect of gravity in the quantum realm in a nonrelativistic way. In this paper, we study the GUP effect on anharmonic oscillator by the ladder operator and perturbation theory. Taking different orders of perturbation from the potential of anharmonic oscillator, the first and second order energy corrections and the first order correction of wavefunction have been derived. We have also studied the variation of energy spectrum in general harmonic and anharmonic oscillator in an undergraduate nonrelativistic approach.

Aspects of Quantum Gravity Phenomenology and Astrophysics

With the discovery of gravitational waves, the search for the quantum of gravity, the graviton, is imminent. We discuss the current status of the bounds on graviton mass from experiments as well as the theoretical understanding of these particles. We provide an overview of current experiments in astrophysics such as the search for Hawking radiation in gamma-ray observations and neutrino detectors, which will also shed light on the existence of primordial black holes. Finally, the semiclassical corrections to the image of the event horizon are discussed.

Three “layers” of graphene monolayer and their analog generalized uncertainty principles

We show that graphene, in its simplest form and settings, is a practical tabletop realization of the analog of exotic quantum gravity scenarios, which are speculated to lead to certain generalized Heisenberg algebras. In particular, we identify three different energy regimes (the ``layers'') where the physics is still of a pseudorelativistic (Dirac) type but more and more sensitive to the effects of the lattice. This plays here a role analog to that of a discrete space, where the Dirac quasiparticles live. This work improves and pushes further earlier results, where the physical meaning of the high energy momenta was clear, but the conjugate coordinates only had a purely abstract description. Here we find the physical meaning of the latter by identifying the mapping between the high energy coordinates and low energy ones, i.e., those measured in the lab. We then obtain two generalized Heisenberg algebras that were not noticed earlier. In these two cases, we have the striking result that the high energy coordinates just coincide with the standard ones, measured in the lab. A third generalized Heisenberg algebra is obtained, and it is an improvement of the results obtained earlier in two respects: we now have an expression of the generalized coordinates in terms of the standard phase-space variables, and we obtain higher order terms. All mentioned results clearly open the doors to tabletop experimental verifications of many generalized uncertainty principle--corrected predictions of the quantum gravity phenomenology.

Weak deflection angle and shadow cast by the charged-Kiselev black hole with cloud of strings in plasma* *Partly supported by the Uzbekistan Ministry for Innovative Development (FZ-20200929344 and F-FA-2021-510). I.H. is grateful to the Institute of Mathematics, University of Aberdeen, Scotland, UK, where a part of this study was done under the IMU-CDC Individual Travel Support Program. G.M. is supported

In this study, the gravitational deflection angle of photons in the weak field limit (or the weak deflection angle) and shadow cast by the electrically charged and spherically symmetric static Kiselev black hole (BH) in the string cloud background are investigated. The influences of the BH charge Q, quintessence parameter γ, and string cloud parameter a on the weak deflection angle are studied using the Gauss-Bonnet theorem, in addition to studying the influences on the radius of photon spheres and size of the BH shadow in the spacetime geometry of the charged-Kiselev BH in string clouds. Moreover, we study the effects of plasma (uniform and non-uniform) on the weak deflection angle and shadow cast by the charged-Kiselev BH surrounded by the clouds of strings. In the presence of a uniform/nonuniform plasma medium, an increase in the string cloud parameter a increases the deflection angle α. In contrast, a decrease in the BH charge Q decreases the deflection angle. Further, we observe that an increase in the BH charge Q causes a decrease in the size of the shadow of the BH. We notice that, with an increase in the values of the parameters γ and a, the size of the BH shadow increases, and therefore, the intensity of the gravitational field around the charged-Kiselev BH in string clouds increases. Thus, the gravitational field of the charged-Kiselev BH in the string cloud background is stronger than the field produced by the pure Reissner-Nordstrom BH. Moreover, we use the data released by the Event Horizon Telescope (EHT) collaboration, for the supermassive BHs M87* and Sgr A*, to obtain constraints on the values of the parameters γ and a.

Relativistic deformed kinematics: From flat to curved spacetimes

Doubly special relativity has been studied for the last 20 years as a way to go beyond the special relativistic kinematics, trying to capture residual effects of a quantum gravity theory. In particular, in doubly special relativity, the Einstenian relativity principle is generalized, adding to the speed of light another relativistic invariant, the Planck energy. There are several papers in the literature showing a connection between this deformed kinematics and a curved momentum space. Here we review how such kinematics can be derived from geometrical ingredients in a rigorous way, and how they can be generalized when regarding a curved spacetime. For the last aim, it is mandatory to consider a particular geometry for all phase-space variables, the so-called generalized Hamilton spaces. This construction allows us to define a spacetime in these theories, which in fact depends on the momenta. Then, starting from such a momentum dependent metric, we also revise several concepts of general relativity, with the final aim of establishing a self-consistent geometrical structure from which quantum gravity phenomenology can be explored.