Limits on quantum gravity effects from Swift short gamma-ray bursts

Abstract

The delay in arrival times between high and low energy photons from cosmic sources can be used to test the violation of the Lorentz invariance (LIV), predicted by some quantum gravity theories, and to constrain its characteristic energy scale E QG that is of the order of the Planck energy. Gamma-ray bursts (GRBs) and blazars are ideal for this purpose thanks to their broad spectral energy distribution and cosmological distances: at first order approximation, the constraints on E QG are proportional to the photon energy separation and the distance of the source. However, the LIV tiny contribution to the total time delay can be dominated by intrinsic delays related to the physics of the sources: long GRBs typically show a delay between high and low energy photons related to their spectral evolution (spectral lag). Short GRBs have null intrinsic spectral lags and are therefore an ideal tool to measure any LIV effect. We considered a sample of 15 short GRBs with known redshift observed by Swift and we estimate a limit on E QG 1.5 × 10 16 GeV. Our estimate represents an improvement with respect to the limit obtained with a larger (double) sample of long GRBs and is more robust than the estimates on single events because it accounts for the intrinsic delay in a statistical sense.

Commutative or noncommutative spacetime? Two length scales of noncommutativity

“…The differences from the conclusions of the authors in Ref. [45] are not, of course, due to any mistake of these authors, but to the fact that they plot the data with respect to a KðzÞ function, whereas here, according to the calculations above, the z dependence is coded by the I 2 ðzÞ function [Eq. (44)].…”

“…Looking for eventual Lorentz-invariance violation (LIV), the authors in Ref. [45] have analyzed 15 short pulses (on the energy bands 50-100 and 150-200 keV), concluding that there is no evidence 6 for energy dependence of the light propagation speed. Here, the same analyzing technique as described above has been applied to the same data with a different conclusion, as shown in Fig.…”

“…. Lags=ð1 þ zÞ vs I 2 ðzÞ ð1þzÞ 3 for the 15 short GRBs in Ref [45]. and fitting lines with three intersects (red) or one intersect (green).…”

Dispersive property of the quantum vacuum and the speed of light

“…different approaches to quantum gravity) in them the Lorentz invariance principle is violated . The swift short gamma ray bursts is an already known example for the energy-dependent velocity of light at smaller energies than the quantum gravity high energy scales [13].…”

“…The Hamiltonian function consists two terms where the first term is the standard well-known function: (13), and the second term is the nonlinear correction: 14).…”