Gaussian models for observed dispersion in high redshift gamma ray bursts

Astronomical observations of gamma-ray bursts commonly exhibit dispersive behavior where high-energy gamma rays arrive significantly later than low-energy photons. Although certain quantum gravity theories suggest such dispersion, the underlying mechanisms are not yet fully understood. Nevertheless, a quadratic polynomial model has been proposed for the frequency-dependent photon velocity. Substituting this model into the Helmholtz equation then leads to a number of candidate forms of the underlying differential equations, where additional terms in the Maxwell equations model the observed dispersion. Unfortunately, this quadratic dispersion model results in unusual behavior such as superluminal velocity. Therefore, a new Gaussian dispersion model is also proposed. This Gaussian model closely approximates the quadratic model at low frequencies while avoiding the superluminal behavior of quadratic models.