Pith. sign in

REVIEW 4 major objections 4 minor 45 references

Discriminating between different modified dispersion relations from gamma-ray observations

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A single parameterized time-delay formula reproduces all polynomial modified dispersion relations used in gamma-ray quantum-gravity searches, and simulations show the inferred Planck-scale limit can vary by an order of magnitude depending…

desk verdict A useful unifying parameterization of MDR time delays, but the simulation-based quantitative claims need a caveat until the GRB 090510 validation gap is resolved. read the letter →

arxiv 2412.16048 v2 pith:WF3SVNXT submitted 2024-12-20 astro-ph.HE gr-qc

S. Caroff , C. Pfeifer , J. Bolmont , T. Terzić , A. Campoy-Ordaz , D. Kerszberg , M. Martinez , U. Pensec
show 3 more authors
C. Plard J. Strišković S. Wong
This is my paper · ORCID
classification astro-ph.HEgr-qc
keywords modifieddispersionrelationstimedelaysgamma-rayburstsactivegalacticnucleiquantumgravityphenomenologyLorentzinvarianceviolationparameterizedlag-redshiftrelationsimulatedobservations
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that gamma-ray time-delay searches for quantum-gravity effects have been tied to a single lag-redshift model, and that this is too narrow. It presents a general parameterization of polynomial modified dispersion relations in a cosmological spacetime, whose associated time-delay formula reduces to a single compact expression, Eq. (25), encompassing existing and new models through the choice of parameter functions $B_m$. Simulations of realistic flaring AGN and gamma-ray burst data show that the lower limit on the energy scale $\Lambda$ can shift by up to an order of magnitude depending on the assumed lag-redshift model, with the standard (JP) model giving the most stringent bound. An injected Planck-scale lag is detected under all models considered, but the inferred magnitude is model-dependent, and one model (DSR2) even flips the sign of the lag, which would mislead about subluminal versus superluminal propagation. The paper concludes that model choice should be treated as a systematic uncertainty and that a source sample evenly spread in redshift is needed to discriminate between models.

What carries the argument

The central object is the parameterized time-delay formula Eq. (25), constructed from the polynomial MDR Hamiltonian $h(t,p_t,w)=p_t^2 \Lambda^{-I} \sum_m B_m(t(z))\, p_t^m w^{I-m}$ (Eq. 18). The functions $B_m$ carry all model information; each choice of $B_m$ turns Eq. (25) into a different lag-redshift relation $\kappa(z)=\int_0^z \frac{\sum_m B_m(z')\,(1+z')^m}{H(z')}\,dz'$. For a fixed leading order $I$, the formula separates the energy dependence $E_{01}^I - E_{02}^I$ from the redshift geometry $\kappa(z)$, so that a single likelihood code can test any polynomial model by swapping $B_m$. This converts the analysis from a single-model search into a model-comparison framework, and it also reveals degeneracies: different dispersion relations can produce the same time delay at first order.

What would settle it

Measure the lag-redshift relation $\kappa(z)$ from two or more flaring sources at very different redshifts with an order-of-magnitude gain in sensitivity: if the inferred $\kappa(z)$ cannot be fitted by any finite set of polynomial coefficients $B_m$, the polynomial parameterization is falsified. A sharper test for the model family: the (DSR2) model predicts a negative time lag for sources at $z<0.95$ for a positive $\Lambda$, so observing a positive lag from a low-redshift AGN while a high-redshift GRB shows a negative lag would rule out that model's sign structure.

Watch

Extended reading notes

Core claim

The central claim is that every polynomial modified dispersion relation of the form $h(t,p_t,w)=p_t^2 \Lambda^{-I} \sum_m B_m(t(z))\, p_t^m w^{I-m}$, evaluated to leading order in $1/\Lambda$, yields a time delay $\Delta t = \frac{I+1}{2}\,\frac{E_{01}^I - E_{02}^I}{\Lambda^I} \int_0^z \frac{\sum_m B_m(z')\,(1+z')^m}{H(z')}\,dz'$. This single formula, Eq. (25), covers the well-known (JP) model, $\kappa$-Poincar\'e-type models, curvature-induced models, and two DSR-inspired models, plus new ones, simply by choosing $B_m$. The paper demonstrates that this choice changes the lag-redshift relation enough that, in lag-free simulated data, the inferred lower limit on $\Lambda$ varies by about an order of magnitude between models; when a Planck-scale lag is injected assuming the standard (JP) model, all other models still detect a lag but assign it a different magnitude, and the (DSR2) model even inverts its sign.

Load-bearing premise

The derivation assumes the quantum-gravity modification of the photon dispersion relation is a polynomial in energy and momentum at a single leading order in $1/\Lambda$, with all redshift dependence carried by the coefficients $B_m(t(z))$; if the true modification is non-polynomial or mixes orders in $\Lambda$, the parameterized time-delay formula and the model comparisons built on it do not apply.

Editorial extensions

If this is right

  • If a time lag is detected, its measured magnitude and the derived energy scale depend on the assumed modified dispersion relation, so limits quoted with the standard model are not directly comparable with limits from other models.
  • A Planck-scale lag injected in the standard (JP) model is detected under all six lag-redshift models considered, but with a biased magnitude; one model (DSR2) would even report a negative lag, inverting the subluminal/superluminal interpretation.
  • Choosing the wrong model can change the lower limit on the quantum-gravity scale by roughly an order of magnitude, so future experimental searches should report limits under multiple models rather than only the standard one.
  • A source sample evenly distributed in redshift is important for discrimination: some models are best separated at low redshift, others at high redshift, so combining AGNs and gamma-ray bursts widens the model-testing power.
  • The parameterization opens the way to fit the coefficients $B_m(t)$ directly to observations, turning a future detection into a model-selection test rather than a single-scale measurement.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the framework is right, the historical single-model limits on $\Lambda$ may carry a systematic bias; re-analyzing archival gamma-ray burst and AGN data with the full family of $B_m$ could convert existing non-detections into a band of model-dependent limits and possibly reveal weak model preferences.
  • Because Eq. (25) is linear in $B_m$, a sufficiently loud lag detection across multiple redshifts would let one reconstruct the shape of $\kappa(z)$ almost non-parametrically, yielding a direct measurement of the redshift dependence of the dispersion-relation correction rather than just a single scale.
  • A natural next step, not taken in the paper, is to inject lags from the other models and check whether the standard (JP) recovery is also biased; the paper only injects the (JP) lag, so the reverse model-robustness is untested.
  • The formalism implicitly assumes Finsler-type Hamiltonian dynamics; if quantum gravity instead predicts non-polynomial dispersion relations (for example exponential or logarithmic), the parameterization would need extension before the same data-comparison machinery applies.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper introduces a general polynomial parameterization of modified dispersion relations (MDRs) in FLRW spacetimes, expressing the first-order photon time delay as Eq. (25) with free redshift-dependent coefficient functions B_m(t(z)). From this parameterization it derives or recovers six I=1 benchmark lag-redshift models: Jacob & Piran (JP), a rescaled kappa-Poincare model (RekaP), curvature-induced DSR (CInd), a spatial-momentum modification (SpaM), and two DSR models (DSR1, DSR2). The authors simulate AGN and GRB datasets with and without injected lags, reconstruct the quantum-gravity scale Lambda with a likelihood fit, and report that the inferred limit varies by up to an order of magnitude across models, that an injected Planck-scale JP lag is detected under all models but with biased magnitude, and that a likelihood-ratio test excludes DSR2 at 4.3 sigma.

Significance. If validated, Eq. (25) is a genuinely useful unifying framework for gamma-ray LIV searches: it reduces the choice of MDR model to a choice of B_m coefficients and makes the redshift dependence of the time delay explicit in a form that can be implemented directly in analysis software. The paper is also transparent about its limitations: it explicitly states that instrument response functions and systematics are neglected and that the GRB 090510 simulation result disagrees with the published Fermi-LAT likelihood result. However, the central numerical claims rest on a simulation and likelihood pipeline that is not yet shown to reproduce real data, and the reported differences are presented without statistical uncertainties. The paper is therefore best assessed as a promising methodological proposal whose quantitative conclusions require further validation before they can be used to interpret real gamma-ray data.

major comments (4)
  1. [Sec. IV A, GRB 090510 comparison] The manuscript itself states that for GRB 090510 the 1000 no-lag simulations give a scale lower than the Planck scale for all models, while the published Fermi-LAT likelihood analysis [26] yields a much stronger constraint, and that the discrepancy is too large to be explained by a simple statistical effect. This is a load-bearing validation failure because the central quantitative claims of Secs. IV A and IV B - the order-of-magnitude model dependence of the limits, the detection of an injected lag under all models, and the 4.3 sigma exclusion of DSR2 - are produced by the same simulation and likelihood pipeline. Please either resolve the discrepancy (for example, by reproducing the [26] result on the real GRB 090510 dataset with the updated software) or demonstrate explicitly that the simplified simulations are nevertheless sufficient for the comparative statements made in the paper.
  2. [Sec. III B, instrument response and systematics] The paper deliberately neglects instrument response functions and nuisance parameters in both simulations and analysis, citing [36] for a typical factor of about 2 weakening of IACT constraints and 10% for Fermi-LAT. These systematic effects are comparable to or larger than several of the reported differences between models (for example, JP versus SpaM or RekaP at low redshift), so the numerical limits in Fig. 2 and the significances in Fig. 4 cannot be assumed to carry over to real data. Please either include response functions in the simulations or explicitly mark all numerical limits and significances as illustrative and provide the model-dependent correction factors.
  3. [Fig. 2 and Sec. IV A, uncertainty on limits] The text says that for GRB 090510 'the one thousand simulations give a scale lower than the Planck scale in all models,' which implies a distribution over realizations, but Fig. 2 shows only single point values with no error bars or spread. Without a measure of the dispersion of the Lambda limits across the 1000 realizations, the claimed factor-of-10 differences between models cannot be assessed for statistical significance. Please add error bars, quantiles, or a separate figure showing the distribution of reconstructed Lambda limits for each model and source.
  4. [Sec. IV B, likelihood-ratio test] The test statistic used to claim exclusion of DSR2 at 4.3 sigma is described only as 'computing the square of the Lcomb(lambda_min) ratio obtained from the (JP) model and each tested model.' This is ambiguous and statistically nonstandard, particularly because the models are non-nested. Please define the test statistic explicitly (for example, 2 Delta ln L), state the null distribution used to convert the value into standard deviations, and justify its applicability to non-nested model comparison.
minor comments (4)
  1. [Fig. 1 caption] The caption contains a duplicated label '(z)*kappa(z)*kappa' in the printed text; this should be corrected.
  2. [Secs. II C and IV A, model notation] The model called 'RekaP' in the equation labels and text appears as 'kP' in Fig. 2; please unify the notation to avoid confusion with the kappa-Poincare bicrossproduct model, which at first order is degenerate with JP.
  3. [Sec. IV A, GRB 090510 discussion] The sentence 'our simulation results are compatible with the uncertainties given in [26] for the Pair View (PV) and Sharpness-Maximization Method (SMM), while reducing the important bias observed for GRB 090510 in the same paper' is unclear in light of the preceding sentence about a large discrepancy with the likelihood result of [26]; please clarify what is meant.
  4. [Eq. (24)] In Eq. (24) the symbol p is used without an explicit statement of whether it is the physical or comoving spatial momentum; please define it consistently to avoid ambiguity in the conversion from the Hamiltonian parameterization to the energy expression.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the parameterized lag framework follows from explicitly stated Hamiltonian ansätze and a prior mathematical lemma, and the simulated limits are outputs of the analysis rather than inputs to the models.

full rationale

The paper's central derivation is not circular. Starting from the perturbed Hamiltonian (11), the general first-order time-delay formula (12)-(13) is imported from [14], an overlapping-author paper. Although this is a self-citation and is load-bearing, the cited result is a parameter-free mathematical lemma with stated assumptions (first-order perturbation in h, FLRW symmetry); it does not assume the polynomial parameterization or any of the target lag formulas. The new step, Eq. (25), is obtained by substituting the explicitly labeled polynomial ansatz (18) into that formula. The individual lag-redshift relations (JP), (SpaM), (RekaP), (CInd), (DSR1), and (DSR2) are then specializations of the coefficient functions B_m, so their differences are consequences of the chosen Hamiltonians, not of fitting. The scale Lambda is the fitted output: simulated datasets are generated either with no lag or with a fixed injected lambda, and the likelihood analysis reconstructs Lambda through Eq. (41); no fitted parameter is renamed as a prediction. The claim that an injected lag is detected under all models is a simulation outcome stemming from the nonzero lag-redshift functions, not a tautology. The paper's own admission of an unresolved discrepancy with the published Fermi-LAT GRB 090510 constraint (Sec. IV A) and the neglect of instrument response and systematics (Sec. III B) are validation and robustness limitations, not circularity: they do not make any prediction equivalent to its inputs. Self-citations to [13], [14], and [36] provide derived formulas and a previously validated analysis method, which count as independent support under the stated rules. No circular step can be exhibited by direct reduction of an output to an input; the appropriate finding is no significant circularity, with only a minor self-citation presence.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The only fitted number is Lambda; the framework itself is built on an assumption of polynomial first-order MDR perturbations. No new particles or forces are introduced.

free parameters (1)
  • Quantum gravity scale Lambda (EQG) = 0.16 E_P (DSR2) to ~1 E_P (JP) for combined lag-free analysis
    The single parameter constrained by the likelihood for each lag-redshift model; all model differences are encoded in kappa*(z), so the Lambda limits are model-dependent.
assumptions (5)
  • ad hoc to paper MDR perturbation is polynomial in p_t and w at a single leading order I of 1/Lambda (Eq. 16, 18)
    Defines which models the framework covers; non-polynomial MDRs or mixed-order models are excluded.
  • domain assumption First-order perturbation theory in h around the FLRW Hamiltonian (Eq. 11)
    The general time-delay formula (12) is valid only to first order in h; higher-order terms are dropped.
  • standard math FLRW cosmology with H(z) = H0 sqrt(Omega_m(1+z)^3 + Omega_Lambda), neglecting radiation and curvature
    Used in all lag integrals and in converting arrival-time differences to redshift; appropriate for z<1 but is an approximation.
  • domain assumption The source emits photons of different energies simultaneously, with no source-intrinsic spectral lag
    The injected and reconstructed lags are attributed entirely to propagation; the paper notes in Sec. V that source-intrinsic delays would need separation.
  • standard math The background formula Eq. (12)-(13) from Pfeifer [14] is correct
    The central time-delay derivation imports this result without re-derivation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Discriminating between different modified dispersion relations from gamma-ray observations." pith.science (2026). https://pith.science/paper/WF3SVNXT

@misc{pith2026241216048,
  author       = {Pith},
  title        = {Pith review of: Discriminating between different modified dispersion relations from gamma-ray observations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WF3SVNXT}},
  note         = {Machine review of arXiv:2412.16048}
}
abstract

The fact that the standard dispersion relation for photons in vacuum could be modified because of their interaction with the quantum nature of spacetime has been proposed more than two decades ago. A quantitative model [Jacob \& Piran, JCAP 01, 031 (2008)], has been tested extensively using distant highly energetic astrophysical sources, searching for energy-dependent time delays in photon arrival times. Since no delay was firmly measured, lower limits were set on the energy scale $\Lambda$ related to these effects. In recent years, however, different but equally well-grounded expressions beyond the Jacob \& Piran model were obtained for the photon dispersion relation, leading to different expressions for the dependence of lag versus redshift. This article introduces a general parameterization of modified dispersion relations in cosmological symmetry, which directly leads to a general parameterized lag versus redshift dependence encompassing both existing and new models. This parameterization could be used in the future to compare the predicted time lags of the different models and test them against observations. To investigate this possibility, realistic data sets are simulated, mimicking different types of extragalactic sources as detected by current and future instruments. When no lag is injected in the simulated data, each lag-redshift model leads, as expected, to a different value for the limit on $\Lambda$, and the Jacob \& Piran model gives the most stringent bound. When a lag at $\Lambda \sim E_P$ in the Jacob \& Piran model is injected, it is detected for all the other lag-redshift relations considered, although leading to different values. Finally, the possibility to discriminate between several lag-redshift models is investigated, emphasizing the importance of an evenly distributed sample of sources across a wide range of redshifts.

Figures

Figures reproduced from arXiv: 2412.16048 by the authors.

Figure 1
Figure 1. FIG. 1. The dimensionless lag-redshift relation [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Lower limit on energy scale Λ as a function of redshift when no lag is injected. The last point on the right shows the [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Reconstructed lag from the combination of all the [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

45 extracted references · 12 canonical work pages

  1. [26]

    Vasileiou, A

    V. Vasileiou, A. Jacholkowska, F. Piron, J. Bolmont, C. Couturier, J. Granot, F. W. Stecker, J. Cohen-Tanugi, and F. Longo, Constraints on Lorentz invariance vi- olation from Fermi-Large Area Telescope observations of gamma-ray bursts, Phys. Rev. D 87, 10.1103/phys- revd.87.122001 (2013), arXiv:1305.3463 [astro-ph.HE]

    arXiv 2013

  2. [36]

    First Combined Study on LIV from Observations of Energy-dependent Time Delays from Multiple-type Gamma-ray Sources -- Part I. Motivation, Method Description and Validation through Simulations of H.E.S.S., MAGIC and VERITAS Datasets

    J. Bolmont, S. Caroff, M. Gaug, A. Gent, A. Ja- cholkowska, D. Kerszberg, C. Levy, T. Lin, M. Mar- tinez, L. Nogu´ es, A. N. Otte, C. Perennes, M. Ronco, and T. Terzi´ c, First Combined Study on Lorentz Invariance Violation from Observations of Energy-dependent Time Delays from Multiple-type Gamma-Ray Sources. I. Moti- vation, Method Description, and Vali...

    work page Pith review arXiv 2022

  3. [1]

    Addazi et al., Quantum gravity phenomenology at the dawn of the multi-messenger era—A review, Prog

    A. Addazi et al., Quantum gravity phenomenology at the dawn of the multi-messenger era—A review, Prog. Part. Nucl. Phys. 125, 103948 (2022), arXiv:2111.05659 [hep- ph]

    arXiv 2022

  4. [2]

    Amelino-Camelia, Quantum-Spacetime Phenomenol- ogy, Living Rev

    G. Amelino-Camelia, Quantum-Spacetime Phenomenol- ogy, Living Rev. Rel. 16, 5 (2013), arXiv:0806.0339 [gr- qc]

    arXiv 2013

  5. [3]

    Kempf, G

    A. Kempf, G. Mangano, and R. B. Mann, Hilbert space representation of the minimal length uncertainty relation, Phys. Rev. D 52, 1108 (1995), arXiv:hep-th/9412167

    arXiv 1995

  6. [4]

    S. Das, E. C. Vagenas, and A. F. Ali, Discreteness of Space from GUP II: Relativistic Wave Equations, Phys. Lett. B 690, 407 (2010), [Erratum: Phys.Lett.B 692, 342–342 (2010)], arXiv:1005.3368 [hep-th]

    work page Pith review arXiv 2010

  7. [5]

    Garattini and G

    R. Garattini and G. Mandanici, Modified Dispersion Re- lations lead to a finite Zero Point Gravitational Energy, Phys. Rev. D 83, 084021 (2011), arXiv:1102.3803 [gr-qc]

    arXiv 2011

  8. [6]

    Amelino-Camelia, N

    G. Amelino-Camelia, N. Loret, and G. Rosati, Speed of particles and a relativity of locality in κ-Minkowski quantum spacetime, Phys. Lett. B 700, 150 (2011), arXiv:1102.4637 [hep-th]

    arXiv 2011

Show all 45 references
  1. [7]

    J. R. Ellis, N. Mavromatos, and D. Nanopoulos, Deriva- tion of a Vacuum Refractive Index in a Stringy Space- Time Foam Model, Phys. Lett. B 665, 412 (2008), arXiv:0804.3566 [hep-th]

    2008 arXiv

  2. [8]

    Gambini and J

    R. Gambini and J. Pullin, Nonstandard optics from quantum space-time, Phys. Rev. D 59, 124021 (1999), arXiv:gr-qc/9809038

    1999 arXiv

  3. [9]

    Alves Batista et al

    R. Alves Batista et al. , White Paper and Roadmap for Quantum Gravity Phenomenology in the Multi- Messenger Era, (2023), arXiv:2312.00409 [gr-qc]

    2023 arXiv

  4. [10]

    J. R. Ellis, N. E. Mavromatos, D. V. Nanopoulos, and A. S. Sakharov, Quantum-gravity analysis of gamma- ray bursts using wavelets, Astron. Astrophys. 402, 409 (2003), arXiv:astro-ph/0210124

    2003 arXiv

  5. [11]

    Jacob and T

    U. Jacob and T. Piran, Lorentz-violation-induced arrival delays of cosmological particles, JCAP 01, 031 (2008), arXiv:0712.2170 [astro-ph]

    2008 arXiv

  6. [12]

    Rosati, G

    G. Rosati, G. Amelino-Camelia, A. Marciano, and M. Matassa, Planck-scale-modified dispersion relations in FR W spacetime, Phys. Rev. D 92, 124042 (2015), arXiv:1507.02056 [hep-th]

    2015 arXiv

  7. [13]

    Barcaroli, L

    L. Barcaroli, L. K. Brunkhorst, G. Gubitosi, N. Loret, and C. Pfeifer, Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes, Phys. Rev. D 95, 024036 (2017), arXiv:1612.01390 [gr-qc]

    2017 arXiv

  8. [14]

    Pfeifer, Redshift and lateshift from homogeneous and isotropic modified dispersion relations, Phys

    C. Pfeifer, Redshift and lateshift from homogeneous and isotropic modified dispersion relations, Phys. Lett. B 780, 246 (2018), arXiv:1802.00058 [gr-qc]

    2018 arXiv

  9. [15]

    Amelino-Camelia, G

    G. Amelino-Camelia, G. Rosati, and S. Bedi´ c, Phenomenology of curvature-induced quantum- gravity effects, Phys. Lett. B 820, 136595 (2021), arXiv:2012.07790 [gr-qc]

    2021 arXiv

  10. [16]

    Amelino-Camelia, D

    G. Amelino-Camelia, D. Frattulillo, G. Gubitosi, G. Rosati, and S. Bedi´ c, Phenomenology of DSR- relativistic in-vacuo dispersion in FLR W spacetime, JCAP 01, 070 (2024), arXiv:2307.05428 [gr-qc]

    2024 arXiv

  11. [17]

    W. B. Atwood et al. (Fermi-LAT), The Large Area Tele- scope on the Fermi Gamma-ray Space Telescope Mission, Astrophys. J. 697, 1071 (2009), arXiv:0902.1089 [astro- ph.IM]

    2009 arXiv

  12. [18]

    Meegan, G

    C. Meegan, G. Lichti, P. N. Bhat, E. Bissaldi, M. S. Briggs, V. Connaughton, R. Diehl, G. Fishman, J. Greiner, A. S. Hoover, A. J. van der Horst, A. von Kienlin, R. M. Kippen, C. Kouveliotou, S. McBreen, W. S. Paciesas, R. Preece, H. Steinle, M. S. Wallace, R. B. Wilson, and C...

    2009 arXiv

  13. [19]

    Gehrels et al

    N. Gehrels et al. (Swift Science), The Swift Gamma-Ray Burst Mission, Astrophys. J. 611, 1005 (2004), [Erratum: Astrophys.J. 621, 558 (2005)], arXiv:astro-ph/0405233

    2004 arXiv

  14. [20]

    Holler, D

    M. Holler, D. Berge, C. van Eldik, J. P. Lenain, V. Marandon, T. Murach, M. de Naurois, R. D. Parsons, H. Prokoph, and D. Zaborov, Observations of the Crab Nebula with H.E.S.S. Phase II, arXiv e-prints , arXiv:1509.02902 (2015), arXiv:1509.02902 [astro-ph.HE]

    2015 arXiv

  15. [21]

    Aleksi´ cet al

    J. Aleksi´ cet al. (MAGIC), The major upgrade of the MAGIC telescopes, Part II: A performance study using observations of the Crab Nebula, Astropart. Phys. 72, 76 (2016), arXiv:1409.5594 [astro-ph.IM]

    2016 arXiv

  16. [22]

    Park (VERITAS), Performance of the VERITAS ex- periment, PoS ICRC2015, 771 (2016), arXiv:1508.07070 [astro-ph.IM]

    N. Park (VERITAS), Performance of the VERITAS ex- periment, PoS ICRC2015, 771 (2016), arXiv:1508.07070 [astro-ph.IM]

    2016 arXiv

  17. [23]

    Zanin et al

    R. Zanin et al. (CTA Observatory, CTA Consortium, LST), CTA – the World’s largest ground-based gamma- ray observatory, PoS ICRC2021, 005 (2022)

    2022

  18. [24]

    Abe et al

    H. Abe et al. (CTA-LST Project), Observations of the Crab Nebula and Pulsar with the Large-sized Telescope Prototype of the Cherenkov Telescope Array, Astrophys. J. 956, 80 (2023), arXiv:2306.12960 [astro-ph.HE]

    2023

  19. [25]

    Ma et al

    X.-H. Ma et al. , Chapter 1 LHAASO Instruments and Detector technology *, Chin. Phys. C 46, 030001 (2022)

    2022

  20. [27]

    Cao et al

    Z. Cao et al. (LHAASO), Stringent Tests of Lorentz Invariance Violation from LHAASO Observations of GRB 221009A, Phys. Rev. Lett. 133, 071501 (2024), arXiv:2402.06009 [astro-ph.HE]

    2024

  21. [28]

    Ellis, R

    J. Ellis, R. Konoplich, N. E. Mavromatos, L. Nguyen, A. S. Sakharov, and E. K. Sarkisyan-Grinbaum, Ro- bust constraint on Lorentz violation using Fermi-LAT gamma-ray burst data, Phys. Rev. D 99, 083009 (2019), arXiv:1807.00189 [astro-ph.HE]

    2019 arXiv

  22. [29]

    Abramowski et al

    A. Abramowski et al. (H.E.S.S. Collaboration), Search for Lorentz Invariance breaking with a likelihood fit of the PKS 2155-304 flare data taken on MJD 53944, Astropart. Phys. 34, 738 (2011), arXiv:1101.3650 [astro-ph.HE]

    2011 arXiv

  23. [30]

    Abe et al

    S. Abe et al. (MAGIC Collaboration), Constraints on Lorentz invariance violation from the extraordinary Mrk 421 flare of 2014 using a novel analysis method, JCAP 2024 (07), 044, arXiv:2406.07140 [astro-ph.HE]

    2014

  24. [31]

    Terzi´ c, D

    T. Terzi´ c, D. Kerszberg, and J. Striˇ skovi´ c, Probing Quan- tum Gravity with Imaging Atmospheric Cherenkov Tele- scopes, Universe 7, 345 (2021), arXiv:2109.09072 [astro- ph.HE]

    2021 arXiv

  25. [32]

    Barcaroli, L

    L. Barcaroli, L. K. Brunkhorst, G. Gubitosi, N. Loret, 13 and C. Pfeifer, Hamilton geometry: Phase space geome- try from modified dispersion relations, Phys. Rev. D 92, 084053 (2015), arXiv:1507.00922 [gr-qc]

    2015 arXiv

  26. [33]

    J. R. Ellis, N. E. Mavromatos, D. V. Nanopoulos, A. S. Sakharov, and E. K. G. Sarkisyan, Robust limits on Lorentz violation from gamma-ray bursts, Astropart. Phys. 25, 402 (2006), [Erratum: Astropart.Phys. 29, 158–159 (2008)], arXiv:0712.2781 [astro-ph]

    2006 arXiv

  27. [34]

    Rodriguez Martinez and T

    M. Rodriguez Martinez and T. Piran, Constraining Lorentz violations with gamma-ray bursts, JCAP04, 006 (2006), arXiv:astro-ph/0601219

    2006 arXiv

  28. [35]

    Navas et al

    S. Navas et al. (Particle Data Group Collaboration), Review of Particle Physics, Phys. Rev. D 110, 030001 (2024)

    2024

  29. [37]

    Albert et al

    J. Albert et al. (MAGIC Collaboration), Variable VHE gamma-ray emission from Markarian 501, Astrophys. J. 669, 862 (2007), arXiv:astro-ph/0702008

    2007 arXiv

  30. [38]

    Mart ´ ınez and M

    M. Mart ´ ınez and M. Errando, A new approach to study energy-dependent arrival delays on photons from astro- physical sources, Astropart. Phys. 31, 226–232 (2009)

    2009

  31. [39]

    Albert et al

    J. Albert et al. (MAGIC Collaboration), Probing Quan- tum Gravity using Photons from a flare of the active galactic nucleus Markarian 501 Observed by the MAGIC telescope, Phys. Lett. B668, 253 (2008), arXiv:0708.2889 [astro-ph]

    2008 arXiv

  32. [40]

    Aharonian et al

    F. Aharonian et al. (H.E.S.S. Collaboration), An Ex- ceptional Very High Energy Gamma-Ray Flare of PKS 2155-304, Astrophys. J. Lett. 664, L71 (2007), arXiv:0706.0797 [astro-ph]

    2007 arXiv

  33. [41]

    V. A. Acciari et al. (MAGIC Collaboration), Teraelec- tronvolt emission from the γ-ray burst GRB 190114C, Nature (London) 575, 455 (2019), arXiv:2006.07249 [astro-ph.HE]

    2019 arXiv

  34. [42]

    V. A. Acciari et al. (MAGIC Collaboration), Observation of inverse Compton emission from a longγ-ray burst, Na- ture (London) 575, 459 (2019), arXiv:2006.07251 [astro- ph.HE]

    2019 arXiv

  35. [43]

    V. A. Acciari et al. (MAGIC Collaboration), Bounds on Lorentz invariance violation from MAGIC observation of GRB 190114C, Phys. Rev. Lett. 125, 021301 (2020), arXiv:2001.09728 [astro-ph.HE]

    2020

  36. [44]

    A. A. Abdo et al. (Fermi LAT Collaboration), A limit on the variation of the speed of light arising from quan- tum gravity effects, Nature (London) 462, 331 (2009), arXiv:0908.1832 [astro-ph.HE]

    2009 arXiv

  37. [45]

    The CTAO Consortium, CTAO performance https: //www.ctao.org/for-scientists/performance/, Ac- cessed: 2024-10-23

    2024

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.