Quantum Gravity Energy Scale Research Articles

Constraints on Lorentz invariance violation from the LHAASO observation of GRB 221009A

In some quantum gravity (QG) theories, Lorentz symmetry may be broken above the Planck scale. The Lorentz invariance violation (LIV) may induce observable effects at low energies and be detected at high energy astrophysical measurements.The Large High Altitude Air Shower Observatory (LHAASO) has detected the onset, rise, and decay phases of the afterglow of GRB 221009A, covering a wide energy range of photons approximately from 0.2 to 13 TeV. This observation provides an excellent opportunity to study the Lorentz invariance violation effect. In this study, we simultaneously utilize the data from the KM2A and WCDA detectors of LHAASO, and apply two event by event methods, namely the pair view method and maximum likelihood method, to investigate LIV. We obtain stringent constraints on the QG energy scale. For instance, through the maximum likelihood method, we determine the 95% confidence level lower limits to be E QG,1 > 14.7 (6.5) × 1019 GeV for the subluminal (superluminal) scenario of n = 1, and E QG,2 > 12.0 (7.2) × 1011 GeV for the subluminal (superluminal) scenario of n = 2. We find that the rapid rise and slow decay behaviors of the afterglow can impose strong constraints on the subluminal scenario, while the constraints are weaker for the superluminal scenario.

Expected signature for the Lorentz invariance violation effects on γ−γ absorption

There are still some significant and unanswered questions about the incredible very-high-energy $\ensuremath{\gamma}$-ray signatures. To help understand the mechanism, focusing on the linear and quadratic perturbation mode for the subluminal regime, we revisit the expected signature for the Lorentz invariance violation (LIV) effects on $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ absorption in the TeV spectra of gamma-ray bursts (GRBs). We note that there is a critical energy for the pair production process, which is sensitive to the assumed quantum gravity energy scale. We suggest that a reemergence of the energy spectrum of $\ensuremath{\gamma}$ rays at several tens of TeV is a rough observational diagnostic for the LIV effects. The expected spectra characteristics are applied to GRB 221009A. The results show that the cosmic opacity with LIV effects considered here can roughly reproduce the observed $\ensuremath{\gamma}$-ray spectra for the source, which enables us to constrain the upper limit of the values of the energy scale to ${E}_{\mathrm{QG},1}\ensuremath{\le}3.35\ifmmode\times\else\texttimes\fi{}{10}^{20}\text{ }\text{ }\mathrm{GeV}$ for the linear perturbation and ${E}_{\mathrm{QG},2}\ensuremath{\le}9.19\ifmmode\times\else\texttimes\fi{}{10}^{12}\text{ }\text{ }\mathrm{GeV}$ for the quadratic perturbation. These scenarios lead to updated bounds on the LIV coefficient, with ${\ensuremath{\xi}}_{1}^{\ensuremath{'}}\ensuremath{\ge}3.62\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ for the linear perturbation and ${\ensuremath{\xi}}_{2}^{\ensuremath{'}}\ensuremath{\ge}1.33\ifmmode\times\else\texttimes\fi{}{10}^{6}$ for the quadratic perturbation, in the standard model extension framework.

First Combined Study on Lorentz Invariance Violation from Observations of Energy-dependent Time Delays from Multiple-type Gamma-Ray Sources. I. Motivation, Method Description, and Validation through Simulations of H.E.S.S., MAGIC, and VERITAS Data Sets

Gamma-ray astronomy has become one of the main experimental ways to test the modified dispersion relations (MDRs) of photons in vacuum, obtained in some attempts to formulate a theory of quantum gravity. The MDRs in use imply time delays that depend on the energy and that increase with distance following some function of redshift. The use of transient, or variable, distant and highly energetic sources already allows us to set stringent limits on the energy scale related to this phenomenon, usually thought to be of the order of the Planck energy, but robust conclusions on the existence of MDR-related propagation effects still require the analysis of a large population of sources. In order to gather the biggest sample of sources possible for MDR searches at teraelectronvolt energies, the H.E.S.S., MAGIC, and VERITAS collaborations enacted a joint task force to combine all their relevant data to constrain the quantum gravity energy scale. In the present article, the likelihood method used to combine the data and provide a common limit is described in detail and tested through simulations of recorded data sets for a gamma-ray burst, three flaring active galactic nuclei, and two pulsars. Statistical and systematic errors are assessed and included in the likelihood as nuisance parameters. In addition, a comparison of two different formalisms for distance dependence of the time lags is performed for the first time. In a second article, to appear later, the method will be applied to all relevant data from the three experiments.

Testing Lorentz Violation with IceCube Neutrinos

Lorentz violation (LV) induced by Quantum Gravity has been tested at much lower energies than the Planck scale with more and more observational evidence. In recent studies, the time of flight difference between the TeV neutrino and MeV photon from Gamma Ray Bursts (GRBs) have been used to constrain the LV energy scale, based on the energy-dependent speed variation. Here, we performed a correlation study between the updated 7.5 year high-energy starting events (HESE), neutrino alert events detected by IceCube, and a full sample of more than 7000 GRBs, and we found six GRB-neutrino candidates, including four alerts and two track events. We obtained the first order energy scale of quantum gravity, namely EQG=8−5+15×1017GeV, which was consistent with other authors‘ work. We suggest that neutrinos and anti-neutrinos can be identified, respectively, due to the delay or advance of the observed time. For future point source search study of neutrinos, the arrival time difference of different particles may have to be taken into account.

Lifshitz scaling in CPT-even Lorentz-violating electrodynamics and GRB time delay

In this work, we consider the Ho\v{r}ava-Lifshitz scaling to rewrite higher-order derivatives in Lorentz-violating CPT-even electrodynamics. The possibility of the Lorentz invariance violation being originally suppressed by the quantum gravity energy scale $M_{\rm QG}$, may be indeed circumvented in a scenario with anisotropy between space and time above certain intermediate energy scale $\Lambda_{\rm HL} \ll M_{\rm QG}$. To test the model, we have used observational results of a cosmological time delay between high and low energy photons from gamma ray bursts (GRB090510) event. For specific values of the Lifshitz critical exponent, we have found interesting lower bounds on the values of $M_{\rm QG}$.

Planck-scale constraints on anisotropic Lorentz and CPT invariance violations from optical polarization measurements

Lorentz invariance is the fundamental symmetry of Einstein's theory of special relativity, and has been tested to great level of detail. However, theories of quantum gravity at the Planck scale indicate that Lorentz symmetry may be broken at that scale motivating further tests. While the Planck energy is currently unreachable by experiment, tiny residual effects at attainable energies can become measurable when photons propagate over sufficiently large distances. The Standard-Model Extension (SME) is an effective field theory approach to describe low-energy effects of quantum gravity theories. Lorentz and CPT symmetry violating effects are introduced by adding additional terms to the Standard Model Lagrangian. These terms can be ordered by the mass dimension of the corresponding operator, and the leading terms of interest have dimension d = 5. Effects of these operators are a linear variation of the speed of light with photon energy, and a rotation of the linear polarization of photons quadratic in photon energy, as well as anisotropy. We analyzed optical polarization data from 72 AGN and GRBs and derived the first set of limits on all 16 coefficients of mass dimension d = 5 of the SME photon sector. Our constraints imply a lower limit on the energy scale of quantum gravity of $10^6$ times the Planck energy, severly limiting the phase space for any theory that predicts a rotation of the photon polarization quadratic in energy.

Limits on the neutrino velocity, Lorentz invariance, and the weak equivalence principle with TeV neutrinos from gamma-ray bursts

Five TeV neutrino events weakly correlated with five gamma-ray bursts (GRBs) were detected recently by IceCube. This work is an attempt to show that if the GRB identifications are verified, the observed time delays between the TeV neutrinos and gamma-ray photons from GRBs provide attractive candidates for testing fundamental physics with high accuracy. Based on the assumed associations between the TeV neutrinos and GRBs, we find that the limiting velocity of the neutrinos is equal to that of photons to an accuracy of ∼ 1.9 × 10−15 – 2.5 × 10−18, which is about 104 – 107 times better than the constraint obtained with the neutrino possibly from a blazar flare. In addition, we set the most stringent limits up to date on the energy scale of quantum gravity for both the linear and quadratic violations of Lorentz invariance, namely EQG, 1 > 6.3 × 1018 – 1.5 × 1021 GeV and EQG, 2 > 2.0 × 1011 – 4.2 × 1012 GeV, which are essentially as good as or are an improvement of one order of magnitude over the results previously obtained by the GeV photons of GRB 090510 and the PeV neutrino from a blazar flare. Assuming that the Shapiro time delay is caused by the gravitational potential of the Laniakea supercluster of galaxies, we also place the tightest limits to date on Einstein's weak equivalence principle through the relative differential variations of the parameterized post-Newtonian parameter γ values for two different species of particles (i.e., neutrinos and photons), yielding Δγ ∼ 10−11 – 10−13. However, it should be emphasized again that these limits here obtained are at best forecast of what could be achieved if the GRB/neutrino correlations would be finally confirmed.

Gamma rays as probes of the Universe

The propagation of γ rays over very large distances provides new insights on the intergalactic medium and on fundamental physics. On their path to the Earth, γ rays can annihilate with diffuse infrared or optical photons of the intergalactic medium, producing e+e− pairs. The density of these photons is poorly determined by direct measurements due to significant galactic foregrounds. Studying the absorption of γ rays from extragalactic sources at different distances allows the density of low-energy diffuse photons to be measured. Gamma-ray propagation may also be affected by new phenomena predicted by extensions of the Standard Model of particle physics. Lorentz Invariance is violated in some models of Quantum Gravity, leading to an energy-dependent speed of light in vacuum. From differential time-of-flight measurements of the most distant γ-ray bursts and of flaring active galactic nuclei, lower bounds have been set on the energy scale of Quantum Gravity. Another effect that may alter γ-ray propagation is predicted by some models of String Theory, namely the mixing of the γ ray with a light fundamental boson called an “axion-like particle”, which does not interact with low-energy photons. Such a mixing would make the Universe more transparent to γ rays than what would otherwise be, in a sense it decreases the amount of modification to the spectrum that comes from the extragalactic background light. The present status of the search for all these phenomena in γ-ray astronomy is reviewed. La propagation des photons γ sur de très grandes distances nous permet de sonder le milieu intergalactique et fournit des tests de physique fondamentale. Au cours de leur chemin vers la Terre, ceux-ci peuvent s'annihiler avec les photons infrarouges et optiques du milieu intergalactique, produisant ainsi des paires e+e−. L'absorption des photons γ émis par des sources extragalactiques à différentes distances permet de mesurer ce fond diffus, par ailleurs très mal connu par des mesures directes en raison des importants rayonnements d'avant-plan dus à la Galaxie. La propagation des photons γ peut aussi être affectée par de nouveaux phénomènes prédits par des extensions du modèle standard de la physique des particules. L'invariance de Lorentz est violée dans certains modèles de gravité quantique où la vitesse de la lumière dans le vide varie avec l'énergie du photon γ. Les mesures différentielles de temps de vol sur les sursauts γ et sur les éruptions de noyaux actifs de galaxie ont permis d'obtenir des bornes inférieures sur l'échelle d'énergie de la gravité quantique. Un autre effet pouvant affecter la propagation des photons γ est prédit par des modèles de la théorie des cordes. Il s'agit du mélange quantique entre le photon et une particule légère de type « axion », qui n'interagit pas avec les photons infrarouge et optiques. En diminuant dans les spectres l'empreinte de l'absorption par le fond diffus, ce mélange rendrait l'Univers plus transparent que prévu aux photons γ. L'article présente l'état actuel des recherches sur l'ensemble de ces phénomènes en astronomie γ

Constraining Lorentz invariance violation from the continuous spectra of short gamma-ray bursts*Supported by National Natural Science Foundation of China (11375203, 11305181, 11322545, 11335012) and Knowledge Innovation Program of The Chinese Academy of Sciences

In some quantum gravity theories, a foamy structure of space-time may lead to Lorentz invariance violation (LIV). As the most energetic explosions in the Universe, gamma-ray bursts (GRBs) provide an effect way to probe quantum gravity effects. In this paper, we use the continuous spectra of 20 short GRBs detected by the Swift satellite to give a conservative lower limit of quantum gravity energy scale MQG. Due to the LIV effect, photons with different energy have different velocities. This will lead to the delayed arrival of high energy photons relative to low energy ones. Based on the fact that the LIV-induced time delay cannot be longer than the duration of a GRB, we present the most conservative estimate of the quantum gravity energy scales from 20 short GRBs. The strictest constraint, MQG > 5.05 × 1014 GeV in the linearly corrected case, is from GRB 140622A. Our constraint on MQG, although not as tight as previous results, is the safest and most reliable so far.

Lorentz invariance violation: The latest Fermi results and the GRB/ AGN complementarity

Because they are bright and distant, Gamma-ray Bursts (GRBs) have been used for more than a decade to test propagation of photons and to constrain relevant Quantum Gravity (QG) models in which the velocity of photons in vacuum can depend on their energy. With its unprecedented sensitivity and energy coverage, the Fermi satellite has provided the most constraining results on the QG energy scale so far. In this talk, the latest results obtained from the analysis of four bright GRBs observed by the Large Area Telescope will be reviewed. These robust results, cross-checked using three different analysis techniques set the limit on QG energy scale at EQG,1>7.6 times the Planck energy for linear dispersion and EQG,2>1.3×1011GeV for quadratic dispersion (95% CL). After describing the data and the analysis techniques in use, results will be discussed and confronted to latest constraints obtained with Active Galactic Nuclei.

Constraints on Lorentz invariance violation fromFermi-Large Area Telescope observations of gamma-ray bursts

We analyze the MeV/GeV emission from four bright Gamma-Ray Bursts (GRBs) observed by the Fermi-Large Area Telescope to produce robust, stringent constraints on a dependence of the speed of light in vacuo on the photon energy (vacuum dispersion), a form of Lorentz invariance violation (LIV) allowed by some Quantum Gravity (QG) theories. First, we use three different and complementary techniques to constrain the total degree of dispersion observed in the data. Additionally, using a maximally conservative set of assumptions on possible source-intrinsic spectral-evolution effects, we constrain any vacuum dispersion solely attributed to LIV. We then derive limits on the "QG energy scale" (the energy scale that LIV-inducing QG effects become important, E_QG) and the coefficients of the Standard Model Extension. For the subluminal case (where high energy photons propagate more slowly than lower energy photons) and without taking into account any source-intrinsic dispersion, our most stringent limits (at 95% CL) are obtained from GRB090510 and are E_{QG,1}>7.6 times the Planck energy (E_Pl) and E_{QG,2}>1.3 x 10^11 GeV for linear and quadratic leading order LIV-induced vacuum dispersion, respectively. These limits improve the latest constraints by Fermi and H.E.S.S. by a factor of ~2. Our results disfavor any class of models requiring E_{QG,1} \lesssim E_Pl.

A unified constraint on the Lorentz invariance violation from both short and long GRBs

Possible Lorentz invariance violation (LIV) has been investigated for a long time based on observations of GRBs. These arguments relied on the assumption that photons with different energy are emitted at the same place and time. In this work, we try to take account of the intrinsic time delay Δtint between emissions of low and high energy photons by using the magnetic jet model. The possible LIV effects are discussed in a unified scenario both for long and short Fermi-detected GRBs. This leads to a unique quantum gravity energy scale M1c2∼1.0×1020GeV respecting the linear dispersion relation.

Robust constraints on Quantum Gravity energy scale with PKS 2155-304 H.E.S.S. data with a likelihood fit

Robust constraints on Quantum Gravity energy scale with PKS 2155-304 H.E.S.S. data with a likelihood fit

Visible borders of spacetime generated by high-energy collisions

Several years ago, two of the present authors proposed the concept of the border of spacetime as a generalization of spacetime singularities. Visible borders of spacetime, which replace naked singularities of classical theory, are not only necessary for the mathematical completeness of general relativity but they also provide a window into new physics of strongly curved spacetime, which is observable in principle. By employing simple geometrical and dimensional arguments, we show that not only black holes but also visible borders of spacetime will be generated at, for example, the CERN Large Hadron Collider, provided that the energy scale of quantum gravity is near 1 TeV in the framework of the large extra-dimension scenario.

THE PROMPT AND HIGH ENERGY EMISSION OF GAMMA RAY BURSTS

I discuss some recent results on the prompt emission of gamma-ray bursts, in particular the jet and radiation properties of the naked-eye burst GRB 080319b, based on Swift and related observations. I then discuss the recent observations by the Fermi satellite of GRB 080916C, the resulting constraints for the bulk Lorentz factor determinations, and the highest lower limit on the quantum gravity energy scale obtained so far.

Measurement of Very High Energy Gamma‐Ray Emission from Four Blazars Using the MAGIC Telescope and a Comparative Blazar Study

The thesis reports on the observation of very high energy gamma radiation from the active galactic nuclei (AGN) Mkn501, 1ES2344, PG1553, and BL Lacertae using the 17 m diameter MAGIC Cherenkov telescope. For the first time, flux variability on a time scale of minutes was observed for Mkn501, allowing the determination of a new limit on the quantum gravity energy scale. This limit is well compatible with the best limits inferred in the literature. 1ES2344 was for the first time observed in a low emission state, whose differential energy spectrum was deduced and whose properties are discussed. PG1553 and BL Lacertae were newly detected at gamma ray energies E>100 GeV. Further a comparative study of all blazar-type AGNs found at E>100 GeV is performed. The thesis also discusses the implementation of a fast repositioning system for the MAGIC telescope and the determination of differential fluxes in the MAGIC standard analysis and reconstruction software.

Can Pulsars be used to Probe Quantum Gravity?

Several radio pulsars have now been shown to emit giant pulses that align in phase with high energy emission rather than with their integrated pulse components. We investigate whether timing of giant and γ-ray pulses can be used to improve limits on the energy scale of quantum gravity by placing bounds on the energy dependence of the speed of light. We find good sources for this experiment are putative Crab-like pulsars in M31, which should in principle be detectable by the current generation of radio telescopes. However, the detection of pulsed emission from their γ-ray counterparts seems unlikely in the near future.

Testing Lorentz Invariance with GRB 021206

Since the discovery of the cosmological origin of gamma-ray bursts (GRBs), there has been growing interest in using these transient events to probe the quantum gravity energy scale in the range 1016-1019 GeV, up to the Planck mass scale. This energy scale can manifest itself through a measurable modification in the electromagnetic radiation dispersion relation for high-energy photons originating from cosmological distances. We have used data from the GRB of 2002 December 6 (GRB 021206) to place an upper bound on the energy dispersion of the speed of light. The limit on the first-order quantum gravity effects derived from this single GRB indicates that the energy scale is in excess of 1.8 × 1017 GeV. We discuss a program to further constrain the energy scale by systematically studying such GRBs.

Severe Limits on Variations of the Speed of Light with Frequency

Explosive astrophysical events at high redshift can be used to place severe limits on the fractional variation in the speed of light with frequency ( $\ensuremath{\Delta}c/c$), the photon mass ( ${m}_{\ensuremath{\gamma}}$), and the energy scale of quantum gravity ( ${E}_{\mathrm{QG}}$). I find $\ensuremath{\Delta}c/cl6.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}$ based on the simultaneous arrival of a flare in GRB 930229 with a rise time of $220\ifmmode\pm\else\textpm\fi{}30\ensuremath{\mu}\mathrm{s}$ for photons of 30 and 200 keV. The limit on ${m}_{\ensuremath{\gamma}}$ is $4.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}44}\mathrm{g}$ for GRB 980703 from radio to gamma ray observations. The limit on ${E}_{\mathrm{QG}}$ is $8.3\ifmmode\times\else\texttimes\fi{}{10}^{16}\mathrm{GeV}$ for GRB 930131 from 30 keV to 80 MeV photons.