Erratum (astro-ph/0510172): Robust Limits on Lorentz Violation from Gamma-Ray Bursts

We correct the fitting formula used in refs. [1,2] to obtain a robust limit on a violation of Lorentz invariance that depends linearly on the photon energy. The correction leads to a slight increase of the limit on the scale of the violation, to M > 1.4 x 10^{16} GeV.Comment: four pages latex, two eps figures, uses special macro

High contrast D1_{1} line electromagnetically induced transparency in nanometric-thin rubidium vapor cell

Electromagnetically induced transparency (EIT) on atomic D$_{1}$ line of rubidium is studied using a nanometric-thin cell with atomic vapor column length in the range of L= 400 - 800 nm. It is shown that the reduction of the cell thickness by 4 orders as compared with an ordinary cm-size cell still allows to form an EIT resonance for $L= \lambda$ ($\lambda =794$ nm) with the contrast of up to 40%. Remarkable distinctions of EIT formation in nanometric-thin and ordinary cells are demonstrated. Despite the Dicke effect of strong spectral narrowing and increase of the absorption for $L=$ $\lambda /2$, EIT resonance is observed both in the absorption and the fluorescence spectra for relatively low intensity of the coupling laser. Well resolved splitting of the EIT resonance in moderate magnetic field for $L=$ $\lambda$ can be used for magnetometry with nanometric spatial resolution. The presented theoretical model well describes the observed results.Comment: Submitted to Applied Physics B: Lasers and Optics, 9 pages, 10 figure

Lorentz Invariance Violation induced time delays in GRBs in different cosmological models

Lorentz Invariance Violation (LIV) manifesting itself by energy dependent modification of standard relativistic dispersion relation has recently attracted a considerable attention. Ellis et al. previously investigated the energy dependent time offsets in different energy bands on a sample of gamma ray bursts and, assuming standard cosmological model, they found a weak indication for redshift dependence of time delays suggestive of LIV. Going beyond the $\Lambda$CDM cosmology we extend this analysis considering also four alternative models of dark energy (quintessence with constant and variable equation of state, Chaplygin gas and brane-world cosmology). It turns out that the effect noticed by Ellis et al. is also present in those models and is the strongest for quintessence with variable equation of state.Comment: 14 pages, 1 figur

GRB 051221A and Tests of Lorentz Symmetry

Various approaches to quantum gravity suggest the possibility of violation of Lorentz symmetry at very high energies. In these cases we expect a modification at low energies of the dispersion relation of photons that contains extra powers of the momentum suppressed by a high energy scale. These terms break boost invariance and can be tested even at relatively low energies. We use the light curves of the very bright short Gamma-Ray Burst GRB 051221A and compare the arrival times of photons at different energies with the expected time delay due to a modified dispersion relation. As no time delay was observed, we set a lower bound of 0.0066 E_{pl} \sim 0.66 10^{17} GeV on the scale of Lorentz invariance violation.Comment: 9 pages, 2 figure

Probing Lorentz Violation in Neutrino Propagation from a Core-Collapse Supernova

Supernova explosions provide the most sensitive probes of neutrino propagation, such as the possibility that neutrino velocities might be affected by the foamy structure of space-time thought to be generated by quantum-gravitational (QG) effects. Recent two-dimensional simulations of the neutrino emissions from core-collapse supernovae suggest that they might exhibit variations in time on the scale of a few milliseconds. We analyze simulations of such neutrino emissions using a wavelet technique, and consider the limits that might be set on a linear or quadratic violation of Lorentz invariance in the group velocities of neutrinos of different energies, v/c = [1 \pm (E/M_{nuLV1})] or [1 \pm (E/M_{\nuLV2})^2], if variations on such short time scales were to be observed, where the mass scales M_{nuLVi} might appear in models of quantum gravity. We find prospective sensitivities to M_{nuLV1} ~ 2 X 10^{13} GeV and M_{nuLV2} ~ 10^6 GeV at the 95% confidence level, up to two orders of magnitude beyond estimates made using previous one-dimensional simulations of core-collapse supernovae. We also analyze the prospective sensitivities to scenarios in which the propagation times of neutrinos of fixed energies are subject to stochastic fluctuations.Comment: 29 pages, 9 figures. A subsection added. The version to appear in Phys. Rev.