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Quantum gravity phenomenology at the dawn of the multi-messenger era—A review
Abstract
The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give us information about their sources in the universe and the properties of the intergalactic medium. Moreover, multi-messenger astronomy opens up the possibility to search for phenomenological signatures of quantum gravity. On the one hand, the most energetic events allow us to test our physical theories at energy regimes which are not directly accessible in accelerators; on the other hand, tiny effects in the propagation of very high energy particles could be amplified by cosmological distances. After decades of merely theoretical investigations, the possibility of obtaining phenomenological indications of Planck-scale effects is a revolutionary step in the quest for a quantum theory of gravity, but it requires cooperation between different communities of physicists (both theoretical and experimental). This review, prepared within the COST Action CA18108 “Quantum gravity phenomenology in the multi-messenger approach”, is aimed at promoting this cooperation by giving a state-of-the art account of the interdisciplinary expertise that is needed in the effective search of quantum gravity footprints in the production, propagation and detection of cosmic messengers.
... When consistency arguments fail to single out a preferred model, experimental input becomes essential. For many years, the inaccessibility of the Planck scale (m pl ∼ 10 19 GeV) seemed to preclude such input. However, increases in control over mesoscopic quantum systems [8][9][10] as well as precision in astrophysical observations [11][12][13][14][15][16] have led to the emergence of quantum gravity phenomenology [17] in the past two decades (see [18,19] for recent reviews). ...
... For many years, the inaccessibility of the Planck scale (m pl ∼ 10 19 GeV) seemed to preclude such input. However, increases in control over mesoscopic quantum systems [8][9][10] as well as precision in astrophysical observations [11][12][13][14][15][16] have led to the emergence of quantum gravity phenomenology [17] in the past two decades (see [18,19] for recent reviews). This program aims to identify potential quantumgravity effects that can be amplified sufficiently to produce measurable corrections at accessible energy scales. ...
Modified dispersion relations (MDRs) and noncommutative geometries are phenomenological models of Planck-scale corrections to relativistic kinematics, motivated by several approaches to quantum gravity. High-energy astrophysical observations, while commonly used to test such effects, are limited by significant systematic uncertainties. In contrast, low-energy, nonrelativistic experiments provide greater control, with precision serving as an amplifier for Planck-suppressed corrections. We derive corrections to Pauli’s equation for nonrelativistic spin-1/2 particles in a magnetic field, incorporating general MDRs and noncommutative geometries. Applying our framework to κ -Poincaré symmetries and minimal-length quantum mechanics, we identify Planck-scale corrections accessible in the nonrelativistic regime. Using the electron’s anomalous magnetic moment, we constrain model parameters, pushing the κ -Poincaré scale in the bi-crossproduct representation beyond 10 10 GeV . These results highlight the complementarity of low-energy precision tests and astrophysical observations in probing quantum gravity phenomenology.
... Since the 1990s, there has been substantial work on experimental and observational searches for hypothetical spacetime-symmetry breaking [19,20], motiviated by theoretical scenarios in which it could arise [21][22][23][24][25]. While no statistical signal for a breakdown of Lorentz, CPT, or diffeomorphism symmetry has yet been found, the "parameter" space of possible effects remains large [12,[26][27][28][29]. ...
In this work, we study a vector model of spontaneous spacetime-symmetry breaking coupled to gravity: the bumblebee model. The primary focus is on static spherically symmetric solutions. Complementing previous work on black hole solutions, we study the effects on the solutions when the vector field does not lie at the minimum of its potential. We first investigate the flat spacetime limit, which can be viewed as a modified electrostatics model with a nonlinear interaction term. We study the stability of classical solutions generally and in the spherically-symmetric case. We also find that certain potentials, based on hypergeometric functions, yield a Hamiltonian bounded from below. With gravity, we solve for the spherically-symmetric metric and vector field, for a variety of choices of the potential energy functions, including ones beyond the quadratic potential like the hypergeometric potentials. Special case exact solutions are obtained showing Schwarszchild-Anti de Sitter and Reissner-Nordstrom spacetimes. We employ horizon and asymptotic analytical expansions along with numerical solutions to explore the general case with the vector field away from the potential minimum. We discover interesting features of these solutions including naked singularities, repulsive gravity, and rapidly varying gravitational field near the source. Finally, we discuss observational constraints on these spacetimes using the resulting orbital behavior.
... This challenging attempt has generated a lot of theoretical as well as phenomenological and experimental efforts, see e.g. [1], [2]. Among many theoretical expectations has emerged a rather widely accepted consensus that Quantum Gravity may likely imply a quantum space-time at some effective regime. ...
The -Minkowski space-time, a Lie-algebraic deformation of the usual Minkowski space-time is considered. A star-product realization of this quantum space-time together with the characterization of the deformed Poincar\'e symmetry acting on it are presented. It is shown that appearance of UV/IR mixing is expected already in scalar field theories on -Minkowski. Classical and one-loop features of a typical gauge theory on this quantum space-time are presented and critically compared to the situation for -Minkowski.
... Quantum deformations of the Minkowski space-time have received considerable attention for more than three decades as they are consensually believed to have a promising physical interest, being of possible relevance in a description of an effective regime of Quantum Gravity [1], [2]. Among these quantum space-times, the κ-Minkowski space-time became from year to year the most popular one in the physical literature [3] due to some of its salient properties, for instance as providing a realization of the Double Special Relativity [4] or its possible relationship to Relative Locality [5], [6]. ...
Poisson structures of the Poincar\'e group can be linked to deformations of the Minkowski space-time, classified some time ago. We construct the star-products and involutions characterizing the -algebras of various quantum Minkowski space-times with non-centrally extended coordinates Lie algebras. We show that the usual Lebesgue integral defines either a trace or a KMS weight ("twisted trace") depending whether the Lie group of the coordinates' Lie algebra is unimodular or not. We determine the Hopf algebras modeling the deformed relativistic symmetries, which appear to be either a deformation of the usual (Hopf) Poincar\'e algebra or a deformation of an enlarged algebra. The results are briefly discussed.
... Such deviations are unmeasurably small. Indeed, no deviation from general relativity has ever been observed, despite intense efforts [151,152]. This strand prediction confirms the predictions from perturbative (relativistic) quantum gravity [146,153]. ...
Any unified description of motion that includes the two Lagrangians of general relativity and of the standard model of particle physics with massive neutrinos must conform to the observed invariant Planck limits for speed, action, entropy, and force. First, these four Planck limits are shown to imply that all observed motion-the motion of black hole horizons , curved space, and quantum particles-results from common unobservable filiform constituents of Planck radius that fluctuate in shape, extend to the cosmological horizon, and follow a fundamental principle combining topology and geometry. For fermions, this closely resembles the description used by Dirac in his lectures. Then, it is shown that such constituents imply black hole entropy and the two Lagrangians. Step by step, it is found that alternative constituents, alternative numbers of dimensions, alternative descriptions of quantum effects and wave functions, alternative gauge groups, alternative elementary particles , alternative Feynman vertices, alternative values of the constants of nature, alternative theories of gravitation, and alternative Lagrangians contradict the observed Planck limits. The constituents imply an upper limit for lepton masses near the tau mass and lead to estimates for the masses of the Higgs and W bosons-possibly the first such derivation from first principles. Thus, only the fundamental principle implies and unifies general relativity and the standard model with massive neutrinos. No deviation from the two Lagrangians is predicted to be observable.
... environment. The fluctuating nature of spacetime (the quantum foam) in a quantum theory of gravity is a commonly cited potential source of a stochastic background that might produce neutrino decoherence effects [40,[44][45][46][47] via interactions of neutrinos with virtual black holes [40]. These Planck-length scale black holes form from extreme fluctuations in the space-time foam and almost immediately evaporate over Planck-time scales. ...
We obtain stringent bounds on neutrino quantum decoherence from the analysis of SN1987A data. We show that for the decoherence model considered here, which allows for neutrino-loss along the trajectory, the bounds are many orders of magnitude stronger than the ones that can be obtained from the analysis of data from reactor neutrino oscillation experiments or neutrino telescopes.
... Moreover, the diverse array of particles within cosmic rays, encompassing protons, electrons, and photons, offers a diverse experimental landscape for exploring various facets of LV (for comprehensive review, refer to Refs. [19,20,21]). ...
Since the early reports of events beyond the Greisen-Zatsepin-Kuzmin (GZK) cutoff, the investigation of ultrahigh-energy cosmic rays has emerged as a fundamental method for testing Lorentz Invariance violation (LV) effects. Recent advances in observational capabilities have resulted in more stringent constraints on LV parameters. This study delves into the potentially anomalous phenomena arising from subluminal and superluminal LV effects, encompassing aspects such as proton decay and atypical threshold behavior of photo-pion production from protons within the GZK region. High-energy proton observations in cosmic rays have imposed stringent constraints on superluminal proton LV effects, while the confirmation of the GZK cutoff has established a robust boundary for the anomalous phenomena associated with subluminal proton LV effects. The research provides rigorously bilateral constraints on proton LV effects from both subluminal and superluminal standpoints.
... In Eq. (1), the second term on the right-handed side is a perturbative expansion of the neutrino mass term, and the third term predicts subtle Lorentz invariance violation (LIV) suppressed by the Planck scale E Pl ≃ 10 19 GeV [43]. Ignoring neutrino-antineutrino mixing, the LIV Lagrangian in the neutrino sector of SME is given by [44]: ...
Recent reactor neutrino oscillation experiments reported precision measurements of and under the standard 3 oscillation framework. However, inter-experiment consistency checks through the parameter goodness-of-fit test reveals proximity to the tension boundary, with the Double Chooz, RENO, and Daya Bay ensemble yielding vs threshold . Anisotropic Lorentz invariance violation (LIV) can accommodate this tension by introducing a location-dependent angle relative to the earth's axis. It is found that anisotropic LIV improve the fit to data up to 1.9 confidence level significance, with the coefficient yielding the best fit, while Parameter Goodness-of-fit (PG) is significantly improved within the LIV formalism.
The propagation of high-frequency gravitational waves can be analyzed using the geometrical optics approximation. In the case of large but finite frequencies, the geometrical optics approximation is no longer accurate and polarization-dependent corrections at first order in wavelength modify the propagation of gravitational waves, via a spin-orbit coupling mechanism. We present a covariant derivation from first principles of effective ray equations describing the propagation of polarized gravitational waves, up to first-order terms in wavelength, on arbitrary spacetime backgrounds. The effective ray equations describe a gravitational spin Hall effect for gravitational waves and are of the same form as those describing the gravitational spin Hall effect of light, derived from Maxwell’s equations.
A bstract
A novel approach to study the properties of models with quantum-deformed relativistic symmetries relies on a noncommutative space of worldlines rather than the usual noncommutative spacetime. In this setting, spacetime can be reconstructed as the set of events, that are identified as the crossing of different worldlines. We lay down the basis for this construction for the κ -Poincaré model, analyzing the fuzzy properties of κ -deformed time-like worldlines and the resulting fuzziness of the reconstructed events.
It is well-known that the universe is opaque to the propagation of Ultra-High-Energy Cosmic Rays (UHECRs) since these particles dissipate energy during their propagation interacting with the background fields present in the universe, mainly with the Cosmic Microwave Background (CMB) in the so-called GZK cut-off phenomenon. Some experimental evidence seems to hint at the possibility of a dilation of the GZK predicted opacity sphere. It is well-known that kinematical perturbations caused by supposed quantum gravity (QG) effects can modify the foreseen GZK opacity horizon. The introduction of Lorentz Invariance Violation can indeed reduce, and in some cases making negligible, the CMB-UHECRs interaction probability. In this work, we explore the effects induced by modified kinematics in the UHECR lightest component phenomenology from the QG perspective. We explore the possibility of a geometrical description of the massive fermions interaction with the supposed quantum structure of spacetime in order to introduce a Lorentz covariance modification. The kinematics are amended, modifying the dispersion relations of free particles in the context of a covariance-preserving framework. This spacetime description requires a more general geometry than the usual Riemannian one, indicating, for instance, the Finsler construction and the related generalized Finsler spacetime as ideal candidates. Finally we investigate the correlation between the magnitude of Lorentz covariance modification and the attenuation length of the photopion production process related to the GZK cut-off, demonstrating that the predicted opacity horizon can be dilated even in the context of a theory that does not require any privileged reference frame.
A theoretical framework for the quantization of gravity has been an elusive Holy Grail since the birth of quantum theory and general relativity. While generations of scientists have attempted to find solutions to this deep riddle, an alternative path built upon the idea that experimental evidence could determine whether gravity is quantized has been decades in the making. The possibility of an experimental answer to the question of the quantization of gravity is of renewed interest in the era of gravitational wave detectors. We review and investigate an important subset of phenomenological quantum gravity, detecting quantum signatures of weak gravitational fields in table-top experiments and interferometers.
In this work, we review the effective field theory framework to search for Lorentz and CPT symmetry breaking during the propagation of gravitational waves. The article is written so as to bridge the gap between the theory of spacetime-symmetry breaking and the analysis of gravitational-wave signals detected by ground-based interferometers. The primary physical effects beyond General Relativity that we explore here are dispersion and birefringence of gravitational waves. We discuss their implementation in the open-source LIGO-Virgo algorithm library suite, and we discuss the statistical method used to perform a Bayesian inference of the posterior probability of the coefficients for symmetry-breaking. We present preliminary results of this work in the form of simulations of modified gravitational waveforms, together with sensitivity studies of the measurements of the coefficients for Lorentz and CPT violation. The findings show the high potential of gravitational wave sources across the sky to sensitively probe for these signals of new physics.
Measurement of the distances to nearby galaxies has improved rapidly in recent decades. The ever-present challenge is to reduce systematic effects, especially as greater distances are probed and the uncertainties become larger. In this paper, we combine several recent calibrations of the tip of the red giant branch (TRGB) method. These calibrations are internally self-consistent at the 1% level. New Gaia Early Data Release 3 data provide an additional consistency check at a (lower) 5% level of accuracy, a result of the well-documented Gaia angular covariance bias. The updated TRGB calibration applied to a sample of Type Ia supernovae from the Carnegie Supernova Project results in a value of the Hubble constant of H0 = 69.8 ± 0.6 (stat) ± 1.6 (sys) km s⁻¹Mpc⁻¹. No statistically significant difference is found between the value of H0 based on the TRGB and that determined from the cosmic microwave background. The TRGB results are also consistent to within 2σ with the SHoES and Spitzer plus Hubble Space Telescope (HST) Key Project Cepheid calibrations. The TRGB results alone do not demand additional new physics beyond the standard (λCDM) cosmological model. They have the advantage of simplicity of the underlying physics (the core He flash) and small systematic uncertainties (from extinction, metallicity, and crowding). Finally, the strengths and weaknesses of both the TRGB and Cepheids are reviewed, and prospects for addressing the current discrepancy with future Gaia, HST, and James Webb Space Telescope observations are discussed. Resolving this discrepancy is essential for ascertaining if the claimed tension in H0between the locally measured and CMB-inferred values is physically motivated.
High energy photons from astrophysical sources are unique probes for some predictions of candidate theories of Quantum Gravity (QG). In particular, Imaging atmospheric Cherenkov telescope (IACTs) are instruments optimised for astronomical observations in the energy range spanning from a few tens of GeV to ∼100 TeV, which makes them excellent instruments to search for effects of QG. In this article, we will review QG effects which can be tested with IACTs, most notably the Lorentz invariance violation (LIV) and its consequences. It is often represented and modelled with photon dispersion relation modified by introducing energy-dependent terms. We will describe the analysis methods employed in the different studies, allowing for careful discussion and comparison of the results obtained with IACTs for more than two decades. Loosely following historical development of the field, we will observe how the analysis methods were refined and improved over time, and analyse why some studies were more sensitive than others. Finally, we will discuss the future of the field, presenting ideas for improving the analysis sensitivity and directions in which the research could develop.
We present new two-sided constraints on the Lorentz Invariance violation energy scale for photons with quartic dispersion relation from recent gamma ray observations by the Tibet-AS γ and LHAASO experiments. The constraints are based on the consideration of the processes of photon triple splitting (superluminal scenario) and the suppression of shower formation (subluminal). The constraints in the subluminal scenario are better than the pair production constraints and are the strongest in the literature.
In this work, we consider a noncommutative (NC) inflationary model with a homogeneous scalar field non-minimally coupled to gravity. We propose to use a canonical deformation between momenta in a spatially flat Friedmann–Le maître–Robertson–Walker universe. This particular choice of noncommutativity allows interesting dynamics that other NC models seem not to allow. In this approach, the dimensional parameter 𝜃, which considered as the length of Planck, presents the quantum regime. But also, it is crucial to recover the standard results by taking the appropriate limits of this parameter. To note that the 1st Friedmann equation remains unaffected while both the Friedmann acceleration and the Klein-Gordon equations are affected by an additional term linear in the NC parameter.
Several studies have been devoted to the possibility that quantum gravity might tangibly affect relativistic kinematics for particles propagating from distant astrophysical sources to our telescopes, but the relevant literature has so far focused exclusively on a subclass of scenarios such that the quantum-gravity effects are independent of (macroscopic) curvature. It was assumed that a phenomenology for quantum-gravity effects that are triggered by curvature might be a dead end because of a double suppression: by the smallness of the characteristic quantum-gravity length scale and by the smallness of curvature. This state of affairs is becoming increasingly unsatisfactory in light of some recent quantum-gravity studies providing evidence of the fact that the presence of curvature might be required in order to have the novel relativistic properties. We here analyze an explicit scenario for curvature-induced quantum-gravity effects, and show that the smallness of curvature does not pose a challenge for phenomenology since it is compensated by the large distances traveled by the particles considered in the relevant phenomenological studies. We also observe that the present data situation for particles propagating from distant astrophysical sources to our telescopes, while inconclusive, provides more encouragement for our curvature-induced effects than for the curvature-independent effects that were so far studied.