Lorentz-violation-induced arrival time delay of astroparticles in Finsler spacetime

Abstract

Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. We present the arrival time delay of astroparticles subject to Lorentz violation in the framework of Finsler geometry, and the result corresponds to that derived by Jacob and Piran in the standard model of cosmology.

Lorentz and CPT breaking in gamma-ray burst neutrinos from string theory

“…In some sense, the D-particle recoil may be viewed as an example of Finsler geometry in string theory. One may define appropriately the Finsler norm from the metric ĝ(V): F = [g αβ (y(V))y α y β ] 1/2 (here y's denote "velocities" in Finslerian frameworks thereof [63]), and discuss geodesics in such space-times as in [63]. However as we have seen above, the effects of D-foam go beyond those encoded in a Finsler-like metric.…”

Trajectories of astroparticles in pseudo-Finsler spacetime with the most general modified dispersion

“…( 16) in pseudo-Finsler spacetime. We use the same method as our previous work [39]: First, we construct the pseudo-Finsler norm of the particle in the expanding universe; Second, we obtain the geodesic equations of the particle; Last, we solve the geodesic equations and calculate the time delay. Since the pseudo-Finsler norm is the most general and more complicated than our previous work [39], the derivation is more complicated.…”

“…where z is the redshift of the source of the two particles, E obs is the observed energy of the high-energy particle from Earth equipment, Ω m and Ω Λ are universe constants, and H 0 is the current Hubble parameter. In our previous research [39], we reconsidered the time difference problem in Finsler spacetime, the result suggested that for the MDR as Eq. ( 1), the arrival time difference formula is surprisingly the same as Eq.…”

Lorentz Symmetry Violation of Cosmic Photons

“…In the development of many quantum gravity theories, physicists absorb the idea of space-time "foam", such as non-critical string theory [33,34], loop quantum gravity [35,36], string theory [37], doubly special relativity [24,25] and the effective field theory approaches [29]. Some space-time structure theories are shown to be feasible of describing quantum gravity, e.g., Li and Chang constructed the theory of gravitation in Berwald-Finsler space [38], and Zhu and Ma got the arrival time delay of LV cosmological particles in the framework of Finsler geometry [39].…”