A new limit on Planck scale Lorentz violation from γ-ray burst polarization
Highlights
► I use GRB polarization data to derive a new constraint on QED dimension-5 Lorentz violations. ► This constraint is an improvement of over 5 orders of magnitude. ► I also derive model independent constraints.
Introduction
Because of the problems associated with merging relativity with quantum theory, it has long been felt that relativity will have to be modified in some way in order to construct a quantum theory of gravitation. Since the Lorentz group is unbounded at the high boost (or high energy) end, in principle it may be subject to modifications in the high boost limit [1], [2]. There is also a fundamental relationship between the Lorentz transformation group and the assumption that space-time is scale-free, since there is no fundamental length scale associated with the Lorentz group. However, as noted by Planck [3], there is a potentially fundamental scale associated with gravity, viz., the Planck scale m, corresponding to an energy (mass) scale of MPl = ℏc/λPl ∼ 1019 GeV.
In recent years, there has been much interest in testing Lorentz invariance violating terms that are of first order in E/MPl, since such terms vanish at very low energy and are amenable to testing at higher energies. In particular, tests using high energy astrophysics data have proved useful in providing constraints on Lorentz invariance violation (LIV) (e.g., see reviews in Refs. [4], [5]).
Section snippets
Vacuum birefringence
Important fundamental constraints on LIV come from searches for the vacuum birefringence effect predicted within the framework of the effective field theory (EFT) analysis of [6] (see also Ref. [7]). Within this framework, applying the Bianchi identities to the leading order Maxwell equations in vacua, a mass dimension 5 operator term is derived of the formIt is shown in Ref. [6] that the expression given in Eq. (1) is the only dimension 5 modification of the free
Previous constraints
A previous bound of ∣ξ∣ ≲ 2 × 10−4, was obtained by Gleiser and Kozameh [10] using the observed 10% polarization of ultraviolet light from a galaxy at distance of around 300 Mpc. Fan et al. used the observation of polarized UV and optical radiation at several wavelengths from the γ-ray bursts (GRBs) GRB020813 at a redshift z = 1.3 and GRB021004 z = 2.3 to get a constraint of ∣ξ∣ ≲ 2 × 10−7 [11]. Jacobson et al. [12] used a report of polarized γ-rays observed [13] in the prompt emission from the γ-ray burst
A new treatment
Unfortunately, despite the many GRBs that have been detected and have known host galaxy spectral redshifts, none of these bursts have measured γ-ray polarization. However, in this paper we take a new approach, deriving an estimated redshift for GRB041219a. This is a GRB with reported polarization but no spectral redshift measurement.
Polarization at a level of 63(+31, −30)% to 96(+39, −40)% in the soft γ-ray energy range has been detected by analyzing data from the spectrometer on INTEGRAL for
Frame independent constraint
The vector n in the EFT model given by Eq. (1) leads to strictly isotropic physics only in one special frame, usually taken to be the frame in which the cosmic microwave background is isotropic. In other frames the dispersion relation will have anisotropic components. This can be taken into account by using the general SME formalism [17]. There are then 16 independent parameters that are weighted by spherical harmonic coefficients according to their spin weight with respect to the line
Other constraints and implications
The Lorentz violating dispersion relation (2) implies that the group velocity of photons, vg = 1 ± ξp/MPl, is energy dependent. This leads to an energy dependent dispersion in the arrival time at Earth for photons spread over a finite energy range originating in a distant source. The result obtained from observations of the γ-ray energy-time profile by the Fermi satellite for the burst GRB090510 gives a limit of ξ < 0.82 [26]. Thus, the time of flight constraint from Fermi, while still significant
Acknowledgements
I would like to thank Neil Gehrels, Sean Scully, Takanori Sakamoto, Tonia Venters, and an anonymous referee for helpful discussions.
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