A nonlinear dynamics for the scalar field in Randers spacetime

TL;DR

This paper explores the behavior of a scalar field in Randers spacetime, revealing nonlinear dynamics, modified dispersion relations, and a tachyon-free spectrum up to second order, driven by Lorentz violation.

Contribution

It introduces a minimal coupling framework for scalar fields in Finslerian Randers spacetime, leading to a novel nonlinear dynamics analysis with perturbative regimes.

Findings

Nonlinear dynamics split into linear and nonlinear regimes.

Modified dispersion relations analyzed with plane-wave solutions.

Spectrum remains free of tachyons up to second-order perturbations.

Abstract

We investigate the properties of a real scalar field in the Finslerian Randers spacetime, where the local Lorentz violation is driven by a geometrical background vector. We propose a dynamics for the scalar field by a minimal coupling of the scalar field and the Finsler metric. The coupling is intrinsically defined on the Randers spacetime, and it leads to a non-canonical kinetic term for the scalar field. The nonlinear dynamics can be split into a linear and nonlinear regimes, which depend perturbatively on the even and odd powers of the Lorentz-violating parameter, respectively. We analyze the plane-waves solutions and the modified dispersion relations, and it turns out that the spectrum is free of tachyons up to second-order.