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