Weak equivalence principle and nonrelativistic limit of general dispersion relations

authored by: Manuel Hohmann, Christian Pfeifer, Fabian Wagner
Abstract: We study the weak equivalence principle in the context of modified dispersion relations, a prevalent approach to quantum gravity phenomenology. We find that generic modified dispersion relations violate the weak equivalence principle. The acceleration in general depends on the mass of the test body, unless the Hamiltonian is either 2-homogeneous in the test particles' 4-momenta or the corresponding Lagrangian differs from the homogeneous case by a total derivative only. The key ingredient of this calculation is a 3+1 decomposition of the parametrization-invariant relativistic test particle action derived from the dispersion relation. Additionally, we apply a perturbative expansion in the test particle's spatial velocity and the inverse speed of light. To quantify our result, we provide a general formula for the Eötvós factor of modified dispersion relations. As a specific example, we study the point-particle motion determined from the κ-Poincaré dispersion relation in the bi-cross-product basis. Comparing the ensuing nonvanishing Eötvós factor to recent data from the MICROSCOPE experiment, we obtain a bound of the model parameter Ξ^-1≥1015 GeV/c2.
External Organisation(s): Center of Applied Space Technology and Microgravity (ZARM)
Type: Article
Journal: Physical Review D
Volume: 110
ISSN: 2470-0010
Publication date: 11.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Nuclear and High Energy Physics
Electronic version(s): https://doi.org/10.1103/PhysRevD.110.104030 (Access: Unknown)

BibTeX

@article{9a12d5d0e4624203af81ea04343b6062,
title = "Weak equivalence principle and nonrelativistic limit of general dispersion relations",
abstract = "We study the weak equivalence principle in the context of modified dispersion relations, a prevalent approach to quantum gravity phenomenology. We find that generic modified dispersion relations violate the weak equivalence principle. The acceleration in general depends on the mass of the test body, unless the Hamiltonian is either 2-homogeneous in the test particles' 4-momenta or the corresponding Lagrangian differs from the homogeneous case by a total derivative only. The key ingredient of this calculation is a 3+1 decomposition of the parametrization-invariant relativistic test particle action derived from the dispersion relation. Additionally, we apply a perturbative expansion in the test particle's spatial velocity and the inverse speed of light. To quantify our result, we provide a general formula for the E{\"o}tv{\'o}s factor of modified dispersion relations. As a specific example, we study the point-particle motion determined from the κ-Poincar{\'e} dispersion relation in the bi-cross-product basis. Comparing the ensuing nonvanishing E{\"o}tv{\'o}s factor to recent data from the MICROSCOPE experiment, we obtain a bound of the model parameter Ξ^-1≥1015 GeV/c2.",
author = "Manuel Hohmann and Christian Pfeifer and Fabian Wagner",
note = "Publisher Copyright: {\textcopyright} 2024 American Physical Society.",
year = "2024",
month = nov,
doi = "10.1103/PhysRevD.110.104030",
language = "English",
volume = "110",
journal = "Physical Review D",
issn = "2470-0010",
publisher = "American Institute of Physics",
number = "10",
}