Lorentz Invariance Violation Parameter Research Articles

Aether-electromagnetic theory and the Casimir effect

In this study, we explore the impact of an additional dimension, as proposed in Kaluza-Klein’s theory, on the Casimir effect within the context of Lorentz invariance violation (LIV), which is represented by the “aether field.” We demonstrate that the Casimir energy is directly influenced by the presence of the fifth dimension, as well as by the aether parameter. Consequently, the force between the plates is also subject to variations of these parameters. Furthermore, we examine constraints on both the size of the extra dimension and the aether field parameter based on experimental data. The LIV parameter can provide insights into addressing the size-related challenges in Kaluza-Klein’s theory and offers a mean to establish an upper limit on the size of the extra dimension. This helps to rationalize the difficulties associated with its detection in current experiments. Published by the American Physical Society 2024

Abnormal threshold behaviors of photo-pion production off the proton in the GZK region

The cosmic-ray spectrum structures help to study the acceleration and propagation mechanism of ultra-high energy cosmic rays, and these structures were predicted to culminate in a cut-off, named the Greisen–Zatsepin–Kuzmin (GZK) cut-off, near 5×1019eV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$5\ imes 10^{19}~\ extrm{eV}$$\\end{document} as a result of the inelastic interaction of protons with the 2.73K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2.73~\ extrm{K}$$\\end{document} black body radiation. The confirmation of the existence of GZK cut-off was tortuous, leading to activities to explore new physics, such as the cosmic-ray new components, unidentified cosmic-ray origins, unknown propagation mechanism and the modification of fundamental physics concepts like the tiny Lorentz invariance violation (LV). The confirmation of the GZK cut-off provides an opportunity to constrain the LV effect. We use a phenomenological framework to restudy the GZK mechanism under the Planck scale deformation of the proton and pion dispersion relations. Restudying the photon induced pion production of the proton p+γ→p+π0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{p}+\\gamma \\rightarrow \ extrm{p}+\\pi ^0$$\\end{document}, we predict abnormal threshold behaviors of this reaction under different LV modifications. Therefore we can study the LV effects not only from the conventional GZK cut-off, but also from potentially threshold anomalies of the pion production process. We divide the LV parameter space into three regions, and analyze the constraints from current observations in each region. The current observations have set strict restrictions on a certain LV region. However, for others LV regions, further experimental observations and theoretical researches are still needed, and we also find survival space for some theoretical explorations that permit specific LV effects.

Constraint on Lorentz invariance violation from Vela pulsar

The High Energy Stereoscopic System (H.E.S.S.) Collaboration reported the discovery of a novel radiation component from the Vela pulsar by their Cherenkov telescopes. It is of great importance that gamma rays with energies of at least 20 TeV are recorded unexpectedly. The H.E.S.S. Collaboration argued that such results may challenge the state-of-the-art models for the high-energy emission of pulsars. We point out in this work that these results also provide a unique opportunity to constrain certain Lorentz invariance violation parameters, leading to the realization of studying Lorentz invariance violation by using gamma-ray pulsars. The Lorentz invariance violation scale is constrained at the level of 1.66\\,\ imes10^{17}$ ?> GeV for the linear scenario, and 3.53\\,\ imes10^{10}$ ?> GeV for the quadratic scenario. We anticipate that digging into the detailed features of the data of the Vela pulsar and analyzing potentially more very-high-energy photon data from pulsars in the future would improve the constraints on Lorentz invariance violation.

Impact of cosmology on Lorentz Invariance Violation constraints from GRB time-delays

Putting constraints on a possible Lorentz Invariance Violation (LIV) from astrophysical sources such as gamma-ray bursts (GRBs) is essential for finding evidences of new theories of quantum gravity (QG) that predict an energy-dependent speed of light. This search has its own difficulties, so usually, the effect of the cosmological model is understudied, with the default model being a fixed-parameters ΛCDM.In this work, we use various astrophysical datasets to study the effect of a number of dark energy models on LIV constraints. To this end, we combine two public time-delay (TD) GRB datasets with the supernovae Pantheon dataset, several measurements of angular baryonic acoustic oscillations (BAO), the cosmic microwave background (CMB) distance prior and an optional GRB or quasars dataset. For the LIV parameter α, we find the expected from previous works average value of , corresponding to GeV for both TD datasets, with the second one being more sensitive to the cosmological model. The cosmology results in a minimum 20% deviation in our constraints on the energy. Interestingly, adding the TD points makes the DE models less-preferable statistically and shifts the value of the parameter down, making it smaller than the expected value. We observe that possible LIV measurements critically depend on the transparency of the assumptions behind the published data concerning cosmology, and taking this into account may be an important contribution in the case of possible detection.

Constraining Lorentz invariance violation with next-generation long-baseline experiments

Unified theories such as string theory and loop quantum gravity allow the Lorentz Invariance Violation (LIV) at the Planck Scale (MP ~ 1019 GeV). Using an effective field theory, this effect can be observed at low energies in terms of new interactions with a strength of ~ 1/MP. These new interactions contain operators with LIV coefficients which can be CPT-violating or CPT-conserving. In this work, we study in detail how these LIV parameters modify the transition probabilities in the next-generation long-baseline experiments, DUNE and Hyper-K. We evaluate the sensitivities of these experiments in isolation and combination to constrain the off-diagonal CPT-violating (aeμ, aeτ, aμτ) and CPT-conserving (ceμ, ceτ, cμτ) LIV parameters. We derive approximate compact analytical expressions of appearance (νμ → νe) and disappearance (νμ → νμ) probabilities in the presence of these LIV parameters to explain our numerical results. We explore the possible correlations and degeneracies between these LIV parameters and the most uncertain 3ν oscillation parameters, namely, θ23 and δCP. We find that for non-maximal values of θ23 (θ23 ≠ 45°), there exist degenerate solutions in its opposite octant for standalone DUNE and Hyper-K. These degeneracies disappear when we combine the data from DUNE and Hyper-K. In case of no-show, we place the expected upper bounds on these CPT-violating and CPT-conserving LIV parameters at 95% C.L. using the standalone DUNE, Hyper-K, and their combination. We observe that due to its access to a longer baseline and multi-GeV neutrinos, DUNE has a better reach in probing all these LIV parameters as compared to Hyper-K. Since the terms containing the CPT-conserving LIV parameters are proportional to neutrino energy in oscillation probabilities, Hyper-K is almost insensitive to the CPT-conserving LIV parameters because it mostly deals with sub-GeV neutrinos.

Investigating the effects of Lorentz Invariance Violation on the CP-sensitivities of the Deep Underground Neutrino Experiment

The phenomena of neutrino oscillations offer a great potential for probing new-physics beyond the Standard Model. Any additional effects on neutrino oscillations can help understand the nature of the non-standard effects. The violation of fundamental symmetries may appear as a probe for new-physics in various neutrino experiments. Lorentz symmetry is one such fundamental symmetry in nature and the breakdown of spacetime is a possible motivation for a departure from the standard Lorentz symmetry picture. The Lorentz invariance violation (LIV) is intrinsic in nature and its effects exist even in a vacuum. Neutrinos can be an intriguing probe for exploring such violations of Lorentz symmetry. The effect of violation of Lorentz invariance can be explored through its impact on the neutrino oscillation probabilities. The effect of LIV is treated as a perturbation to the standard neutrino Hamiltonian considering the Standard Model Extension (SME) framework. In this work, we have probed the effects of LIV on the measurement of neutrino oscillation parameters considering Deep Underground Neutrino Experiment (DUNE) as a case study. The inclusion of LIV affects the measurements of various neutrino oscillation parameters as it modifies the standard neutrino oscillation probabilities. We looked into the capability of DUNE in constraining the LIV parameters and then explored the impact of CPT-violating LIV terms on the mass-induced neutrino oscillation probabilities. We have also probed the impact of LIV parameters on the CP-measurement sensitivities at DUNE.

Distinguishing nonstandard interaction and Lorentz invariance violation at the Protvino to super-ORCA experiment

As the two phenomena nonstandard interaction (NSI) in neutrino propagation and Lorentz invariance violation (LIV) modify the Hamiltonian of neutrino oscillation in a similar fashion, it is very difficult to distinguish these two effects. The only difference between them lies in the fact that NSI depends on the matter density, whereas LIV is independent of the earth matter effect. Therefore for a fixed baseline experiment, where matter density is constant, the theories describing NSI and LIV are exactly equivalent. However, as the present and future bounds of the NSI and LIV parameters are not equivalent, one can distinguish these two scenarios in the long-baseline neutrino experiments depending on their statistics with respect to the present and future bounds of these parameters. In this paper, we attempt to differentiate between LIV and NSI in the context of DUNE and P2SO, as these two future experiments are believed to be sensitive to the strongest matter effect and will have very large statistics. Taking LIV in the data and NSI in theory, our results show that indeed it is possible to have good discrimination between LIV and NSI. The best separation between LIV and NSI at $3\ensuremath{\sigma}\text{ }\text{ }\mathrm{C}.\mathrm{L}.$ is achieved for the parameter ${a}_{\ensuremath{\mu}\ensuremath{\mu}}$ with P2SO. In this case, the value of the LIV parameter, for which separation is possible, lies within its future bound if one considers the value of NSI parameter to be constrained by the present experiments. Between DUNE and P2SO, the latter has better sensitivity for such discrimination.

Investigating Lorentz Invariance Violation with the long baseline experiment P2O

One of the basic propositions of quantum field theory is Lorentz invariance. The spontaneous breaking of Lorentz symmetry at a high energy scale can be studied at low energy extensions like the Standard model in a model-independent way through effective field theory (EFT). The present and future Long-baseline neutrino experiments can give a scope to observe such a Planck-suppressed physics of Lorentz invariance violation (LIV). A proposed long baseline experiment, Protvino to ORCA (dubbed “P2O”) with a baseline of 2595 km, is expected to provide good sensitivities to unresolved issues, especially neutrino mass ordering. P2O can offer good statistics even with a moderate beam power and runtime, owing to the very large (~ 6 Mt) detector volume at KM3NeT/ ORCA. Here we discuss in detail, how the individual LIV parameters affect neutrino oscillations at P2O and DUNE baselines at the level of probability and derive analytical expressions to understand interesting degeneracies and other features. We estimate ∆χ2 sensitivities to the LIV parameters, analyzing their correlations among each other, and also with the standard oscillation parameters. We calculate these results for P2O alone and also carry out a combined analysis of P2O with DUNE. We point out crucial features in the sensitivity contours and explain them qualitatively with the help of the relevant probability expressions derived here. Finally we estimate constraints on the individual LIV parameters at 95% confidence level (C.L.) intervals stemming from the combined analysis of P2O and DUNE datasets, and highlight the improvement over the existing constraints. We also find out that the additional degeneracy induced by the LIV parameter aee around −22 × 10−23 GeV is lifted by the combined analysis at 95% C.L.

LIV effects on the quantum stochastic motion in an acoustic FRW-geometry

It is well known in the literature that vacuum fluctuations can induce a random motion of particles which is sometimes called quantum Brownian motion or quantum stochastic motion. In this paper, we consider Lorentz Invariance Violation (LIV) in an acoustic spatially flat Friedman–Robertson–Walker (FRW) geometry. In particular, we are looking for the LIV effects in the stochastic motion of scalar and massive test particles. This motion is induced by a massless quantized scalar field on this geometry, which in turn is derived from an Abelian Higgs model with LIV. Deviations in the velocity dispersion of the particles proportional to the LIV parameter are found.

Effective electromagnetic actions for Lorentz violating theories exhibiting the axial anomaly

The CPT odd contribution to the effective electromagnetic action deriving from the vacuum polarization tensor in a large class of fermionic systems exhibiting Lorentz invariance violation (LIV) is calculated using thermal field theory methods, focusing upon corrections depending on the chemical potential. The systems considered exhibit the axial anomaly and their effective actions are described by axion electrodynamics whereby all the LIV parameters enter in the coupling Θ(x) to the unmodified Pontryagin density. A preliminary application to type-I tilted Weyl semimetals is briefly presented.

Probing Lorentz Invariance Violation with atmospheric neutrinos at INO-ICAL

The possibility of Lorentz Invariance Violation (LIV) may appear in unified theories, such as string theory, which allow the existence of a new space-time structure at the Planck scale (Mp ∼ 1019 GeV). This effect can be observed at low energies with a strength of ∼ 1/Mp using the perturbative approach. In the minimal Standard Model extension (SME) framework, the neutrino mass-induced flavor oscillation gets modified in the presence of LIV. The Iron Calorimeter (ICAL) detector at the proposed India-based Neutrino Observatory (INO) offers a unique window to probe these LIV parameters by observing atmospheric neutrinos and antineutrinos separately over a wide range of baselines in the multi-GeV energy range. In this paper, for the first time, we study in detail how the CPT-violating LIV parameters (aμτ, aeμ, aeτ) can alter muon survival probabilities and expected μ− and μ+ event rates at ICAL. Using 500 kt·yr exposure of ICAL, we place stringent bounds on these CPT-violating LIV parameters at 95% C.L., which are slightly better than the present Super-Kamiokande limits. We demonstrate the advantage of incorporating hadron energy information and charge identification capability at ICAL while constraining these LIV parameters. Further, the impact of the marginalization over the oscillation parameters and choice of true values of sin2θ23 on LIV constraints is described. We also study the impact of these LIV parameters on mass ordering determination and precision measurement of atmospheric oscillation parameters.

Testing effects of Lorentz invariance violation in the propagation of astroparticles with the Pierre Auger Observatory

Lorentz invariance violation (LIV) is often described by dispersion relations of the form E i 2 = m i 2+p i 2+δi,n E 2+n with delta different based on particle type i, with energy E, momentum p and rest mass m. Kinematics and energy thresholds of interactions are modified once the LIV terms become comparable to the squared masses of the particles involved. Thus, the strongest constraints on the LIV coefficients δi,n tend to come from the highest energies. At sufficiently high energies, photons produced by cosmic ray interactions as they propagate through the Universe could be subluminal and unattenuated over cosmological distances. Cosmic ray interactions can also be modified and lead to detectable fingerprints in the energy spectrum and mass composition observed on Earth. The data collected at the Pierre Auger Observatory are therefore possibly sensitive to both the electromagnetic and hadronic sectors of LIV. In this article, we explore these two sectors by comparing the energy spectrum and the composition of cosmic rays and the upper limits on the photon flux from the Pierre Auger Observatory with simulations including LIV. Constraints on LIV parameters depend strongly on the mass composition of cosmic rays at the highest energies. For the electromagnetic sector, while no constraints can be obtained in the absence of protons beyond 1019 eV, we obtain δγ,0 > -10-21, δγ,1 > -10-40 eV-1 and δγ,2 > -10-58 eV-2 in the case of a subdominant proton component up to 1020 eV. For the hadronic sector, we study the best description of the data as a function of LIV coefficients and we derive constraints in the hadronic sector such as δhad,0 < 10-19, δhad,1 < 10-38 eV-1 and δhad,2 < 10-57 eV-2 at 5σ CL.

Exploring the Violation of Lorentz Invariance using Atmospheric Neutrinos at INO-ICAL

We explore the signature of Lorentz Invariance Violation (LIV) in the Standard Model Extension framework by observing the atmospheric neutrinos and antineutrinos separately with the help of magnetized Iron Calorimeter (ICAL) detector at the proposed India-based Neutrino Observatory (INO). Using 500 kt-yr exposure of ICAL, we place stringent bounds on the CPT-violating LIV parameters α μτ , α ॉμ , and aeT (one-at-a-time) at 95% C.L. (1 d.o.f). We demonstrate the advantages of charge identification capability and hadron energy information at ICAL while constraining these LIV parameters. We also explore interesting correlations among various LIV parameters.

Tunnelling radiation and the microstates of a black hole influenced by the Lorentz invariance violation

In this paper, we have employed the second-order Lorentz invariance violation (LIV) to carefully investigate the effect of quantum gravity on the Hawking radiation of the Dirac particle via tunneling from the Kerr black hole. Firstly, it turns out that the Hawking temperature is not only related to the angular momentum and mass of the black hole, but related to the energy and mass of the emitted particle. In particular, we find that the effective temperature is bigger and bigger with the increase of the energy ω, the angular momentum j and the LIV parameter l p , but is smaller and smaller with the increase of the black hole mass M. Also, it further shows that, although quantum gravity speeds up the black-hole evaporation, it will not evaporate completely, instead a remaining mass, temperature and entropy are left. Finally, through a careful count of the number of the microstates taken away by the black-hole radiation, the initial and remaining number of microstates for the Schwarzschild black hole are presented with the inclusion of the LIV-induced quantum gravity effects.

Can Lorentz invariance violation affect the sensitivity of deep underground neutrino experiment?

We examine the impact of Lorentz Invariance Violation (LIV) in measuring the octant of theta _{23} and CP phases in the context of the Deep Underground Neutrino Experiment (DUNE). We consider the CPT-violating LIV parameters involving e - mu (a_{emu }) and e - tau (a_{etau }) flavors, which induce an additional interference term in neutrino and antineutrino appearance probabilities. This new interference term depends on both the standard CP phase delta and the new dynamical CP phase varphi _{emu }/varphi _{etau }, giving rise to new degeneracies among (theta _{23}, delta , varphi ). Taking one LIV parameter at-a-time and considering a small value of |a_{emu }| = |a_{etau }| = 5 times 10^{-24} GeV, we find that the octant discovery potential of DUNE gets substantially deteriorated for unfavorable combinations of delta and varphi _{emu }/varphi _{etau }. The octant of theta _{23} can only be resolved at 3sigma if the true value of sin ^2theta _{23} lesssim 0.42 or > rsim 0.62 for any choices of delta and varphi . Interestingly, we also observe that when both the LIV parameters a_{emu } and a_{etau } are present together, they cancel out the impact of each other to a significant extent, allowing DUNE to largely regain its octant resolution capability. We also reconstruct the CP phases delta and varphi _{emu }/varphi _{etau }. The typical 1sigma uncertainty on delta is 10–15^{circ } and the same on varphi _{emu }/varphi _{etau } is 25–30^{circ } depending on the choices of their true values.

Exploring the effect of Lorentz invariance violation with the currently running long-baseline experiments

Neutrinos are the fundamental particles, blind to all kind of interactions except the weak and gravitational. Hence, they can propagate very long distances without any deviation. This characteristic property can thus provide an ideal platform to investigate Planck suppressed physics through their long distance propagation. In this work, we intend to investigate CPT violation through Lorentz invariance violation (LIV) in the long-baseline accelerator based neutrino experiments. Considering the simplest four-dimensional Lorentz violating parameters, for the first time, we obtain the sensitivity limits on the LIV parameters from the currently running long-baseline experiments T2K and hbox {NO}nu hbox {A}. In addition to this, we show their effects on mass hierarchy and CP violation sensitivities by considering hbox {NO}nu hbox {A} as a case study. We find that the sensitivity limits on LIV parameters obtained from T2K are much weaker than that of hbox {NO}nu hbox {A} and the synergy of T2K and hbox {NO}nu hbox {A} can improve these sensitivities. All these limits are slightly weaker (2 sigma level) compared to the values extracted from Super-Kamiokande experiment with atmospheric neutrinos. Moreover, we observe that the mass hierarchy and CPV sensitivities are either enhanced or deteriorated significantly in the presence of LIV as these sensitivities crucially depend on the new CP-violating phases. We also present the correlation between sin ^2 theta _{23} and the LIV parameter |a_{alpha beta }|, as well as delta _{CP} and |a_{alpha beta }|.

Optimal estimation of parameters for scalar field in an expanding spacetime exhibiting Lorentz invariance violation

We address the optimal estimation of quantum parameters, in the framework of local quantum estimation theory, for a massive scalar quantum field in the expanding Robertson–Walker universe exhibiting Lorentz invariance violation (LIV). We find that, in the estimation of cosmological parameters, the ultimate bounds to the precision of the Lorentz-invariant massive scalar field can be improved due to the effects of LIV under some appropriate conditions. We also show that, in the Lorentz-invariant massive scalar field and massless scalar field due to LIV backgrounds, the optimal precision can be achieved by choosing the particles with some suitable LIV, cosmological and field parameters. Moreover, in the estimation of LIV parameter during the spacetime expansion, we prove that the appropriate momentum mode of field particles and larger cosmological parameters can provide us a better precision.

Entropy production due to Lorentz invariance violation

It is generally believed that the concept of the spacetime continuum should be modified for distances as small as the Planck length. This is a length scale at which the spacetime might have a discrete structure and quantum gravity effects are dominant. Presumably, the microscopic fluctuations within the geometry of spacetime should result in an enormous entropy production. In the present work, we look for the effects of Lorentz invariance violation (LIV) in flat and curved backgrounds that can be measured by quantum entanglement and quantum thermodynamic entropies for scalar modes. Our results show that the general behavior of these entropies is the same. We also consider variations of the entropies with respect to LIV and cosmological and field parameters. Using the properties of these entropies, along with detecting the most entangled modes, we extract information about the past existence of LIV, which in turn might be useful in recovering the quantum structure of gravity. Indeed, the occurrence of a peak in the behavior of these entropies for a specific momentum could provide information about the expansion parameters. Moreover, information about the LIV parameter is codified in this peak.

Propagation of superluminal PeV IceCube neutrinos: A high energy spectral cutoff or new constraints on Lorentz invariance violation

The IceCube observation of cosmic neutrinos with ${E}_{\ensuremath{\nu}}&gt;60\text{ }\text{ }\mathrm{TeV}$, most of which are likely of extragalactic origin, allows one to severely constrain Lorentz invariance violation (LIV) in the neutrino sector, allowing for the possible existence of superluminal neutrinos. The subsequent neutrino energy loss by vacuum ${e}^{+}{e}^{\ensuremath{-}}$ pair emission (VPE) is strongly dependent on the strength of LIV. In this paper we explore the physics and cosmology of superluminal neutrino propagation. We consider a conservative scenario for the redshift distribution of neutrino sources. Then by propagating a generic neutrino spectrum, using Monte Carlo techniques to take account of energy losses from both VPE and redshifting, we obtain the best present constraints on LIV parameters involving neutrinos. We find that ${\ensuremath{\delta}}_{\ensuremath{\nu}e}={\ensuremath{\delta}}_{\ensuremath{\nu}}\ensuremath{-}{\ensuremath{\delta}}_{e}\ensuremath{\le}5.2\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}21}$. Taking ${\ensuremath{\delta}}_{e}\ensuremath{\le}5\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}21}$, we then obtain an upper limit on the superluminal velocity fraction for neutrinos alone of $1.0\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}20}$. Interestingly, by taking ${\ensuremath{\delta}}_{\ensuremath{\nu}e}=5.2\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}21}$, we obtain a cutoff in the predicted neutrino spectrum above 2 PeV that is consistent with the lack of observed neutrinos at those energies, and particularly at the Glashow resonance energy of 6.3 PeV. Thus, such a cutoff could be the result of neutrinos being slightly superluminal, with ${\ensuremath{\delta}}_{\ensuremath{\nu}}$ being $(0.5\text{ }\text{ }\text{to}\text{ }\text{ }1.0)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}20}$.

Equations for massless and massive spin-1/2 particles with varying speed and neutrino in matter

The modified Dirac equations describing massless and massive spin-1/2 particles violating the Lorentz invariance are considered. The equation for massless fermions with varying speed is formulated in the 16-component first-order form. The projection matrix, which is the density matrix, extracting solutions to the equation has been obtained. Exact solutions to the equation and energy spectrum for a massive neutrino are obtained in the presence of background matter. We have considered as subluminal as well as superluminal propagations of neutrinos. The bounds on the Lorentz invariance violation parameter from astrophysical observations by IceCube, OPERA, MINOS collaborations and by the SN1987A supernova are obtained for superluminal neutrinos.