18 research outputs found

    Modified Theories of Gravity and Cosmological Applications

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    This reprint focuses on recent aspects of gravitational theory and cosmology. It contains subjects of particular interest for modified gravity theories and applications to cosmology, special attention is given to Einstein–Gauss–Bonnet, f(R)-gravity, anisotropic inflation, extra dimension theories of gravity, black holes, dark energy, Palatini gravity, anisotropic spacetime, Einstein–Finsler gravity, off-diagonal cosmological solutions, Hawking-temperature and scalar-tensor-vector theories

    Recent Advances in Single-Particle Tracking: Experiment and Analysis

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    This Special Issue of Entropy, titled “Recent Advances in Single-Particle Tracking: Experiment and Analysis”, contains a collection of 13 papers concerning different aspects of single-particle tracking, a popular experimental technique that has deeply penetrated molecular biology and statistical and chemical physics. Presenting original research, yet written in an accessible style, this collection will be useful for both newcomers to the field and more experienced researchers looking for some reference. Several papers are written by authorities in the field, and the topics cover aspects of experimental setups, analytical methods of tracking data analysis, a machine learning approach to data and, finally, some more general issues related to diffusion

    Quantum gravity phenomenology at the dawn of the multi-messenger era—A review

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    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.publishedVersio

    Quantum gravity phenomenology at the dawn of the multi-messenger era-A review.

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    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. (C) 2022 The Authors. Published by Elsevier B.V

    Quantum gravity phenomenology at the dawn of the multi-messenger era—A review

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    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

    Quantum gravity phenomenology at the dawn of the multi-messenger era : a review

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    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

    Quantum gravity phenomenology at the dawn of the multi-messenger era—A review

    Get PDF
    The exploration of the universe has recently entered a new era thanks to the multimessenger 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.Talent Scientific Research Program of College of Physics, Sichuan University 1082204112427Fostering Program in Disciplines Possessing Novel Features for Natural Science of Sichuan University 2020SCUNL2091000 Talent program of Sichuan province 2021Xunta de GaliciaEuropean Commission European Union ERDF, "Maria de Maeztu'' Units of Excellence program MDM-2016-0692Red Tematica Nacional de Astroparticulas RED2018-102661-TLa Caixa Foundation 100010434European Commission 847648 LCF/BQ/PI21/11830030 754510Ministry of Education, Science & Technological Development, Serbia 451-03-9/2021-14/200124FSR Incoming Postdoctoral Fellowship Ministry of Education, Science and Technological Development, Serbia 451-03-9/2021-14/200124University of Rijeka grant uniri-prirod-18-48Croatian Science Foundation (HRZZ) IP-2016-06-9782Villum Fonden 29405 DGA-FSE 2020-E2117REuropean Regional Development Fund through the Center of Excellence (TK133) "The Dark Side of the Universe'' European Regional Development Fund (ESIF/ERDF)Ministry of Education, Youth & Sports - Czech Republic CoGraDS-CZ.02.1.01/0.0/0.0/15 003/0000437Blavatnik grantBasque Government IT-97916 Basque Foundation for Science (IKERBASQUE)European Space Agency C4000120711 4000132310FNRS (Belgian Fund for Research)Programa de Apoyo a Proyectos de Investigacion e Innovacion Tecnologica (PAPIIT)Universidad Nacional Autonoma de Mexico TA100122National University of La Plata X909 DICYT 042131GRNational Research, Development & Innovation Office (NRDIO) - Hungary 123996FQXiSwiss National Science Foundation (SNSF)European Commission 181461 199307Netherlands Organization for Scientific Research (NWO) 680-91-119 15MV71Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT) Japan Society for the Promotion of ScienceGrants-in-Aid for Scientific Research (KAKENHI) 20H01899 20H05853 JP21F21789Estonian Research Council PRG356Julian Schwinger FoundationGeneralitat Valenciana Excellence PROMETEO-II/2017/033 PROMETEO/2018/165Istituto Nazionale di Fisica Nucleare (INFN)European ITN project HIDDeN H2020-MSCA-ITN-2019//860881-HIDDeNSwedish Research CouncilEuropean Commission 2016-05996 European Research Council (ERC) European Commission 668679Advanced ERC grant TReXMinistry of Education, Universities and Research (MIUR) 2017X7X85KFonds de la Recherche Scientifique - FNRS 4.4501.18Ministry of Research, Innovation and Digitization - Romania PN19-030102-INCDFM PN-III-P4ID-PCE-2020-2374United States Department of Energy (DOE) DE-SC0020262Ministry of Science, ICT & Future Planning, Republic of Korea 075-15-2020-778German Academic Scholarship Foundation German Research Foundation (DFG) 408049454 420243324 425333893 445990517 Germany's Excellence Strategy (EXC 2121 "Quantum Universe'') 390833306 390837967 Federal Ministry of Education & Research (BMBF) 05 A20GU2 05 A20PX1Centro de Excelencia "Severo Ochoa'' SEV-2016-0588CERCA program of the Generalitat de CatalunyaAgencia de Gestio D'Ajuts Universitaris de Recerca Agaur (AGAUR) Generalitat de Catalunya 2017-SGR-1469 2017-SGR-929 ICCUB CEX2019-000918-MNational Science Centre, Poland 2019/33/B/ST2/00050 2017/27/B/ST2/01902Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPQ) 306414/2020-1Dicyt-USACH 041931MFNational Science Fund of Bulgaria KP-06-N 38/11 RCN ROMFORSK 302640Comunidad de Madrid 2018-T1/TIC-10431 2019-T1/TIC-13177 S2018/NMT-4291UK Research & Innovation (UKRI)Science & Technology Facilities Council (STFC) ST/T000759/1 ST/P000258/1 ST/T000732/1 ST/V005596/1Portuguese Foundation for Science and Technology UIDB/00618/2020 UIDB/00777/2020 UIDP/00777/2020 CERN/FIS-PAR/0004/2019 PTDC/FIS-PAR/29436/2017 PTDC/FISPAR/31938/2017 PTDC/FIS-OUT/29048/2017 SFRH/BD/137127/2018Centre National de la Recherche Scientifique (CNRS), LabEx UnivEarthS ANR-10-LABX-0023 ANR18-IDEX-0001Junta de Andalucia European Commission A-FQM-053-UGR18Natural Sciences and Engineering Research Council of Canada (NSERC) RGPIN-2021-03644National Science Centre Poland Sonata Bis 2019/33/B/ST2/00050 DEC-2017/26/E/ST2/00763Natural Sciences and Engineering Research Council of Canada (NSERC) DGIID-DGA 2015-E24/2Spanish Research State Agency and Ministerio de Ciencia e Innovacion MCIN/AEI PID2019-104114RB-C32 PID2019-105544GB-I00 PID2019-105614GB-C21 PID2019106515GB-I00 PID2019-106802GB-I00 PID2019-107394GB-I00 PID2019-107844GB-C21 PID2019-107847RB-C41 MCIN/AEI PGC2018-095328-B-I00 PGC2018-094856-B-I00 PGC2018-096663-B-C41 PGC2018-096663-B-C44 PGC2018-094626-BC21 PGC2018-101858-B-I00 FPA2017-84543-P FPA2016-76005-C2-1-PSpanish 'Ministerio de Universidades' BG20/00228 Spanish Government PID2020-115845GBI00 Generalitat de Catalunya Comunidad de Madrid S2018/NMT-4291 Spanish Government PID2019-105544GB-I00Perimeter Institute for Theoretical PhysicsGovernment of Canada through the Department of Innovation, Science and Economic DevelopmentProvince of Ontario through the Ministry of Colleges and UniversitiesIstituto Nazionale di Fisica Nucleare (INFN)Centre National de la Recherche Scientifique (CNRS)Netherlands Organization for Scientific Research (NWO)Fundamental Questions Institute (FQXi)European Cooperation in Science and Technology (COST) CA18108Research Council of University of GuilanIniziativa Specifica TEONGRAV Iniziativa Specifica QGSKY Iniziativa Specifica QUAGRAP Iniziativa Specifica GeoSymQFTthe Spanish Research State Agency and Ministerio de Ciencia e Innovacion MCIN/AEI PID2020-115845GBI00 PID2019-108485GB-I00 PID2020-113334GB-I00 PID2020-113701GB-I00 PID2020-113775GB-I00 PID2020-118159GB-C41 PID2020-118159GA-C42 PRE2019-089024Rothchild grant UID/MAT/00212/2020 FPU18/0457

    Quantum gravity phenomenology at the dawn of the multi-messenger era-A review

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    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. (C) 2022 The Authors. Published by Elsevier B.V.Peer reviewe

    Progress in Group Field Theory and Related Quantum Gravity Formalisms

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    Following the fundamental insights from quantum mechanics and general relativity, geometry itself should have a quantum description; the search for a complete understanding of this description is what drives the field of quantum gravity. Group field theory is an ambitious framework in which theories of quantum geometry are formulated, incorporating successful ideas from the fields of matrix models, ten-sor models, spin foam models and loop quantum gravity, as well as from the broader areas of quantum field theory and mathematical physics. This special issue collects recent work in group field theory and these related approaches, as well as other neighbouring fields (e.g., cosmology, quantum information and quantum foundations, statistical physics) to the extent that these are directly relevant to quantum gravity research

    Quantum space-time: theory and phenomenology

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    Modern physics is based on two fundamental pillars: quantum mechanics and Einstein's general relativity. Even if, when taken separately, they can claim success in describing satisfactorily a plenty of physical phenomena, so far any attempt to make them compatible with each other failed. It is a central goal of theoretical physics to find a common approach to coherently merge quantum theory and general relativity. Such an effort is not only motivated by the conceptual necessity of completeness that imposes us to look for a unified theoretical framework that gives a consistent picture at all scales, but also by the existence of physical regimes we can not fully describe without a quantum theory of gravity, e.g. the first instants of early universe cosmology. This problem has remained open for more than eighty years now and keeps challenging physicists that, in the struggle to find a solution, have proposed a myriad of models, none of whom can claim full success. In fact, mainly due to the lack of experimental hints, the landscape of quantum gravity currently looks like a variegated compound of approaches that start from different conceptual premises and use different mathematical formalisms. In the majority of cases, it is not clear whether different models reach compatible predictions or even if they produce observable outcomes at all. Given the impossibility to achieve a unique acknowledged theory, it is of pivotal importance to seek insightful connections between different approaches. Such a strategy may help identifying few promising hot spots that may catalyze forthcoming efforts in the quantum gravity research community. In particular, more synergy between top-down and bottom-up models is certainly needed. Besides shedding light on some formal aspects of the models and eventually giving further support to specific ideas, reducing the gap between full-fledged quantum gravity proposals and simpler models that try to capture at least some expected features might produce tangible progress in the field of quantum gravity phenomenology. Indeed, it is now well-established that some effects introduced genuinely at the Planck scale by heuristic models can be efficiently investigated in ongoing and forthcoming experiments. Moreover, the exciting era of multi-messenger and multi-wavelength has started where several satellites, telescopes, and new generation detectors are furnishing us with an incomparable amount of data to probe the structure of gravity on cosmological scales and in new regimes which had remained inaccessible. Finding ways to rigorously derive Planckian testable effects from quantum gravity theories is then needed to enter another phase of maturity of quantum gravity phenomenology, i.e. the passage from the search for Planck-scale signals to the falsification of actual theories. This thesis represents a small step in this direction. To put this plan into action, we start recognizing that, despite the aforementioned heterogeneity, there is the common expectation that near the Planck scale our description of the spacetime as a smooth continuum, a picture shared by both general relativity and quantum mechanics, should break down and be replaced by some ``fuzzy" structure we generically refer to as \textit{quantum spacetime}. Again there are different ways to implement such an idea in different models, however we feel that the most relevant feature that characterizes spacetime quantization from a physical point of view is the associated departure from classical spacetime symmetries that most significantly encode spacetime's properties. In this regard, in the literature of the last three decades there has been much interest in the development of deformations of the Poincar\'e symmetries of special relativity, which most notably took the form of \textit{quantum groups} or \textit{Hopf algebras}, with the aim of modeling Planck scale physics. However, almost the totality of these studies is confined to the limit where gravitational effects are negligible, i.e. a sort of ``quantum Minkowski regime". With the objective to bridge quantum gravity and, in general, beyond general relativity theories with quantum or non-standard Minkowski spacetime models we here devote our attention to the symmetry content of general relativity, synthesized in the \textit{hypersurface deformation algebra}, and explore possible deformations caused by non-classical spacetime effects. Candidate modifications of the algebra of diffeomorphisms have been already obtained in some recent analyses, others will be derived in this thesis for the first time. We then translate modifications of the hypersurface deformation algebra into corresponding deviations from special relativistic symmetry with the main objective of looking for phenomenological opportunities. In particular, studying the Minkowski limit of deformed diffeomorphism algebras, we shall infer two much studied Planckian phenomena, namely \textit{modified dispersion relation} and \textit{the running of spacetime dimensions} with the probed scale. In this thesis we focus in particular on four different paths toward the characterization of non-classical (to be meant in a general sense as non-standard) spacetime properties: \textit{noncommutative geometry}, \textit{loop quantum gravity}, \textit{multifractional geometry}, and \textit{non-Riemannian geometry}; only the second being widely recognized as a candidate full-fledged quantum gravity theory. We first motivate why these two phenomenological Planck scale effects, i.e. dimensional reduction and modifications of particles' dispersion in vacuum, can be ascribed to spacetime fuzziness or quantization intended as an intrinsic obstruction to the measurability of spacetime distances below the Planck scale, an effect which can be deduced from the heuristic combination of general relativistc and quantum mechanical principles. Modified dispersion relation is derived rigorously in the framework of noncommutative geometries and we discuss two different noncommutative models which are of interest for this thesis: Ξ\theta-Minkowski and Îș\kappa-Minkowski. The phenomenon of dimensional flow is instead presented from the perspective of multifractional geometry. Within this framework we show how dimensional flow and spacetime fuzziness are deeply connected. We illustrate how the assumption of an anomalous scaling of the spacetime dimension in the ultraviolet and a slow change of the dimension in the infrared is enough to produce a scale-dependent deformation of the integration measure with also a fuzzy spacetime structure. We also compare the multifractional correction to lengths with the types of Planckian uncertainty for distance and time measurements. This may offer an explanation why dimensional flow is encountered in almost the totality of quantum gravity models. We then introduce the (classical) hypersurface deformation algebra and constructively present two different ways of deriving it which we designate as representations of the algebra: the gravitational constraint representation, where the brackets are reproduced by the time and spatial diffeomorphism generators, and the Gaussian vector field representation, in which the algebra can be read off from the Lie bracket involving the components of a certain class of vector fields. Using this second realization, we study possible Drinfeld twists of space-time diffeomorphisms with Hopf-algebra techniques. We consider both deformed and twisted diffeomorphisms and compute the associated hypersurface deformation algebra. We then turn our attention to recent loop-qauntum-gravity-inspired studies that have motivated a restricted class of modifications of the algebra of gravitational constraints. We discuss these new results in the light of the possibility to identify an effective quantum-spacetime picture of loop quantum gravity, applicable in the Minkowski regime, where the large-scale (coarse-grained) spacetime metric is flat. We show that these symmetry-algebra results are consistent with a description of spacetime given in terms of the Îș\kappa-Minkowski noncommutative spacetime, whose relevance for the study of the quantum-gravity problem has already been proposed for independent reasons. We exploit this unexpected link to extract viable testable predictions out of loop quantum gravity models. These loop-qauntum-gravity-inspired corrections to spacetime symmetries are used to analyze both the consequences on particle propagation and on dimensional running. Adopting a different strategy, we also construct a set of three operators suitable for identifying coordinate-like quantities on a spin-network configuration on the kinematical Hilbert space. Computing their action on coherent coarse-grained states, we are able to study some relevant properties such us the spectra, which are discrete. After that we scrutinize the symmetry structure of multifractional theories with either weighted or qq- derivatives. These theories have the property that the spacetime dimensions are anomalous since they change with the scale of observation. Despite their different mathematical formalisms, both noncommutative and multifractional geometries allow for the spacetime dimension to vary with the probed scale. For this reason, we compare their symmetries and prove that, despite the presence of many contact points claimed by precedent studies, they are are physically inequivalent, yet one can describe certain aspects of Îș\kappa-Minkowski noncommutative geometry as a multifractional theory and vice versa. Turning gravity on, we calculate the algebras of gravitational first-class constraints in the multifractional theories with qq- and weighted derivatives and discuss their differences with respect to the deformed algebras of Îș\kappa-Minkowski spacetime and of loop quantum gravity. Finally, with the aim of traducing multiscale formal properties into physical effects, we derive black hole solution in multifractional gravity theories and highlight new properties in the horizon structure as well as in the thermodynamical properties. Potential phenomenological signatures are underlined. The fourth non-standard spacetime approach we consider is given by non-Riemannian geometries with non-metricity. Among other reasons to modify classical general relativity, one motivation is that modified Einstein-Hilbert action could provide either a better behaved theory in the ultraviolet, while Einstein's theory is not renormalizable, or encode effective corrections to classical gravity, which could be remnants of quantum effects at low energy scales. In this context it is often claimed that a relaxation of the Riemannian condition to incorporate geometric quantities such as torsion and non-metricity may allow to explore new physics associated with defects in a sort of ``spacetime microstructure". We show that non-metricity modifies particles' equations of motion. In particular, we find that it produces observable effects in quantum fields in the form of 4-fermion contact interactions. The analysis we present is carried out in the framework of a wide class of theories of gravity in the metric-affine approach having a modified Lagrangian of the form L(gΌΜ,gΌρR(ρΜ))\mathcal{L}(g_{\mu\nu}, g^{\mu\rho}R_{(\rho \nu)}). Finally, we compute the non-metric deformations of the hypersurface deformation algebra by using the Gaussian-vector-field method and make a qualitative comparison with loop quantum gravity results. The final part of this thesis is dedicated to the search for quantum spacetime effects on the propagation of very-high energy particles in the form of in-vacuo dispersion, i.e. a linear correlation between time of observation and energy of particles. Motivated by some recent studies that exposed rather strong statistical evidence of in-vacuo-dispersion-like spectral lags for gamma-ray bursts in the energy range above 40 GeV, we analyze 7 gamma-ray burst events detected by Fermi-LAT in the period 2008-2016 by extending the window of the statistical analysis down to 5 GeV. Intriguingly, we find results that are consistent with what had been previously noticed at higher energies and, thus, could be of quantum-spacetime origin. Reduced samples of the data set based on different energy cuts are also considered with the objective to strengthen the results of the study. Besides the obvious interest of the feature we find, the main importance of our study stands in the fact that it represents one of the first analyses done over a collection of gamma-ray burst events. This paves the way to statistical analyses needed to produce more robust and reliable results despite huge uncertainties on the astrophysical mechanisms behind the formation, the emission and the propagation of photons produced in gamma-ray explosions
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