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Register a new userTests of Lorentz Invariance Using High Energy Astrophysics Observations
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Floyd W. Stecker
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High-energy astrophysics observations provide the best possibilities to detect a very small violation of Lorentz invariance, such as may be related to the structure of space-time near the Planck scale. I discuss the possible signatures of Lorentz invariance violation that can be manifested by observing the spectra, polarization, and timing of gamma-rays from active galactic nuclei and gamma-ray bursts. Other sensitive tests are provided by observations of the spectra of ultrahigh-energy cosmic rays and very high-energy neutrinos. I also discuss a new time-of-flight analysis of observations of GRB 090510 by the Fermi gamma-ray Space Telescope. These results, based on high-energy astrophysical observations, have fundamental implications for space-time physics and quantum gravity models.
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We discuss some of the tests of Lorentz symmetry made possible by astrophysical observations of ultrahigh energy cosmic rays, gamma-rays, and neutrinos. These are among the most sensitive tests of Lorentz symmetry violation because they are the highest energy phenomena known to man.
Modern astrophysics, especially at GeV energy scales and above is a typical example where several disciplines meet: The location and distribution of the sources is the domain of astronomy. At distances corresponding to significant redshift cosmological aspects such as the expansion history come into play. Finally, the emission mechanisms and subsequent propagation of produced high energy particles is at least partly the domain of particle physics, in particular if new phenomena beyond the Standard Model are probed that require base lines and/or energies unattained in the laboratory. In this contribution we focus on three examples: Highest energy cosmic rays, tests of the Lorentz symmetry and the search for new light photon-like states in the spectra of active galaxies.
The detection of the high-energy ($sim290$ TeV) neutrino coincident with the flaring blazar TXS 0506+056, the first and only $3sigma$ neutrino-source association to date, provides new, multimessenger tests of the weak equivalence principle (WEP) and Lorentz invariance. Assuming that the flight time difference between the TeV neutrino and gamma-ray photons from the blazar flare is mainly caused by the gravitational potential of the Laniakea supercluster of galaxies, we show that the deviation from the WEP for neutrinos and photons is conservatively constrained to have an accuracy of $10^{-6}-10^{-7}$, which is 3--4 orders of magnitude better than previous results placed by MeV neutrinos from supernova 1987A. In addition, we demonstrate that the association of the TeV neutrino with the blazar flare sets limits on the energy scales of quantum gravity for both linear and quadratic violations of Lorentz invariance (LIV) to $E_{rm QG, 1}>3.2times10^{15}-3.7times10^{16}$ GeV and $E_{rm QG, 2}>4.0times10^{10}-1.4times10^{11}$ GeV. These improve previous limits on both linear and quadratic LIV energy scales in neutrino propagation by 5--7 orders of magnitude.
The IceCube observation of cosmic neutrinos with $E_{ u} > 60$ 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 $e^+e^-$ 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 $delta_{ u e} = delta_{ u} - delta_e le 5.2 times 10^{-21}$. Taking $delta_e le 5 times 10^{-21}$, we then obtain an upper limit on the superluminal velocity fraction for neutrinos alone of $1.0 times 10^{-20}$. Interestingly, by taking $delta_{ u e} = 5.2 times 10^{-21}$, 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 $delta_{ u}$ being $(0.5 {rm to} 1.0) times 10^{-20}$.
The GZK cutoff predicted at the Ultra High Energy Cosmic Ray (UHECR) spectrum as been observed by the HiRes and Auger experiments. The results put severe constraints on the effect of Lorentz Invariance Violation(LIV) which has been introduced to explain the absence of GZK cutoff indicated in the AGASA data. Assuming homogeneous source distribution with a single power law spectrum, we calculate the spectrum of UHECRs observed on Earth by taking the processes of photopion production, $e^+e^-$ pair production and adiabatic energy loss into account. The effect of LIV is also taken into account in the calculation. By fitting the HiRes monocular spectra and the Auger combined spectra, we show that the LIV parameter is constrained to $xi=-0.8^{+3.2}_{-0.5}times10^{-23}$ and $0.0^{+1.0}_{-0.4}times10^{-23}$ respectively, which is well consistent with strict Lorentz Invariance up to the highest energy.
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