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Including the metric fluctuations of a realistic cosmological geometry wereconsider an earlier suggestion that measuring the relative time-of-flight ofultra-relativistic particles can provide interesting constraints on fundamentalcosmological and/or particle parameters. Using convenient properties of thegeodetic light-cone coordinates we first compute, to leading order in theLorentz factor and for a generic (inhomogeneous, anisotropic) space-time, therelative arrival times of two ultra-relativistic particles as a function oftheir masses and energies as well as of the details of the large-scalegeometry. Remarkably, the result can be written as an integral over theunperturbed line-of-sight of a simple function of the local, inhomogeneousredshift. We then evaluate the irreducible scatter of the expected data-pointsdue to first-order metric perturbations, and discuss, for an ideal source ofultra-relativistic particles, the resulting attainable precision on thedetermination of different physical parameters.

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