Model-independent constraints on Lorentz invariance violation via the cosmographic approach

Abstract

Since Lorentz invariance plays an important role in modern physics, it is of interest to test the possible Lorentz invariance violation (LIV). The time-lag (the arrival time delay between light curves in different energy bands) of Gamma-ray bursts (GRBs) has been extensively used to this end. However, to our best knowledge, one or more particular cosmological models were assumed a priori in (almost) all of the relevant works in the literature. So, this makes the results on LIV in those works model-dependent and hence not so robust in fact. In the present work, we try to avoid this problem by using a model-independent approach. We calculate the time delay induced by LIV with the cosmic expansion history given in terms of cosmography, without assuming any particular cosmological model. Then, we constrain the possible LIV with the observational data, and find weak hints for LIV.As is well known, Lorentz invariance plays an important role in modern physics. Actually, it is one of the foundation stones of special/general relativity and particle physics, which have been well tested in solar system and colliders. If Lorentz invariance is violated, the pillars of modern physics will be shocked and new physics is needed. So, it is of interest to test the possible Lorentz invariance violation (LIV) with various terrestrial experiments and astrophysical/cosmological observations [1,2].In the literature, there exist many theories inducing LIV. Here we are interested in the possible violation of Lorentz invariance induced by quantum gravity (QG). Commonly, most theories of QG (e.g. string theory, loop quantum gravity, doubly special relativity) predict that LIV might happen on high energy scales [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]49]. The propagation of high energy photons through the spacetime foam might exhibit a non-trivial dispersion relation in vacuum (which should be regarded as a non-trivial medium in QG). The deformed dispersion relation for photons usually takes the form, where E QG is the effective QG energy scale, f is a dimensionless function depending on the particular QG model, c is the limiting speed of light on low energy scales, p and E are the momentum and energy of photons, respectively. On low energy scales E ≪ E QG , one can consider a series expansion of this dispersion relation, namely. Such a series expansion corresponds to an energy-dependent speed ofSo, the high and low energy photons will not reach us at the same time. A signal of energy E that travels a distance L acquires a time delay (measured with respect to the ordinary case of an energy-independent speed c), namely ∆t ∼ ξ(E/E QG )(L/c). Although the QG effect is expected to be very weak (since E QG is typically close to the Planck energy scale E P ∼ 10 19 GeV), a very long distance L can still make it testable. In the pioneer work [3], Amelino-Camelia et al. proposed that Gamma-ray bursts (GRBs) at a cosmological distance can be used to test the possible LIV, while time-lag (the arrival time delay between light curves in diff...

Testing Fundamental Physics with Astrophysical Transients

“…[119,120] extended this analysis to different cosmological models and showed that the result is insensitive to the adopted background cosmology. Subsequently, some cosmology-independent approaches were applied to probe the possible LIV effects [121,122].…”

Tests of Lorentz Invariance

“…[66,67] extended this analysis to other different cosmological models, finding the result is only weakly sensitive to the background cosmology. Some cosmology-independent techniques were furthermore applied to this kind of analysis [68,69].…”

Constraints on quantum gravity and the photon mass from gamma ray bursts

“…for the massive photon. We will assume a ΛCDM cosmology to determine the Hubble parameter H(z); in general one should consider a variety of cosmological models [45][46][47][48], although this is beyond the scope of this work. In both cases we see that the parameter of interest (E QG or m γ ) and the observed energy bands appear as scaling factors.…”