Abstract
Observables which would indicate a modified vacuum dispersion relations, possibly caused by quantum gravity effects, are a four momentum dependence of the cosmological redshift and the existence of a so called lateshift effect for massless or very light particles. Existence or non-existence of the latter is currently analyzed on the basis of the available observational data from gamma-ray bursts and compared to predictions of specific modified dispersion relation models. We consider the most general perturbation of the general relativistic dispersion relation of freely falling particles on homogeneous and isotropic spacetimes and derive the red- and lateshift to first order in the perturbation. Our result generalizes the existing formulae in the literature and we find that there exist modified dispersion relations causing both, one or none of the two effects to first order.
Highlights
Most information about the properties of gravity are obtained by probing the geometry of spacetime through the observation of freely falling particles
In gamma-ray bursts (GRBs) this assumption is not necessarily realized and one has to take into account that the observed lateshift ∆tobs = ∆tm + ∆tǫ + ∆tint is composed of an arrival delay due to the particles mass ∆tm, the lateshift caused by the modified dispersion relations (MDR) ∆tǫ, and, in addition, a difference in the emission time of particle of different momentum due to the mechanism of the GRB itself ∆tint [30]
With help of the new general first order formulae obtained here it was possible to demonstrate that there exist particular MDRs in which only one or none of the effects appear
Summary
Most information about the properties of gravity are obtained by probing the geometry of spacetime through the observation of freely falling particles. Quantum gravity effects are expected to become relevant at the Planck scale and particles with energies closer to the. As long as a fundamental theory of quantum gravity is not available to predict this effect from the scattering between gravitons and the probe particles such quantum gravity effects can be modeled phenomenologically by a modification of the relativistic dispersion relation of freely falling point particles, see [2,3,4,5,6,7,8,9,10,11,12] and references therein. In particular observations from high redshift gamma-ray bursts (GRBs) are candidates to find traces of Planck scale induced modified dispersion relations (MDR) [13,14,15,16]. To deduce a MDR from the measured time of arrival data of neutrinos and photons from GRBs a derivation of the lateshift effect from a most general modification of the general relativistic dispersion relation is required. As an interesting insight from the general red- and lateshift formula we findMDRs which predict both aforementioned effects, only one of them or even none to first order
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