Time of flight of ultra-relativistic particles in a realistic Universe: a viable tool for fundamental physics?

TL;DR

This paper investigates how measuring the time-of-flight of ultra-relativistic particles in a realistic, inhomogeneous universe can constrain fundamental physics parameters, accounting for metric fluctuations and large-scale geometry effects.

Contribution

It provides a leading-order calculation of relative arrival times in an inhomogeneous universe using geodetic light-cone coordinates, including metric perturbations.

Findings

Relative arrival times depend on local redshift and large-scale geometry.

Metric perturbations introduce an irreducible scatter in measurements.

Potential for precise constraints on cosmological and particle physics parameters.

Abstract

Including the metric fluctuations of a realistic cosmological geometry we reconsider an earlier suggestion that measuring the relative time-of-flight of ultra-relativistic particles can provide interesting constraints on fundamental cosmological and/or particle parameters. Using convenient properties of the geodetic light-cone coordinates we first compute, to leading order in the Lorentz factor and for a generic (inhomogeneous, anisotropic) space-time, the relative arrival times of two ultra-relativistic particles as a function of their masses and energies as well as of the details of the large-scale geometry. Remarkably, the result can be written as an integral over the unperturbed line-of-sight of a simple function of the local, inhomogeneous redshift. We then evaluate the irreducible scatter of the expected data-points due to first-order metric perturbations, and discuss, for an ideal source of ultra-relativistic particles, the resulting attainable precision on the determination of different physical parameters.