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

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.

6 pages, 2 figures, Typos corrected, clarifications and a reference added. Version accepted for publication in Physics Letter B

References in corpus (4)

• Big-Bang Nucleosynthesis
• Do stochastic inhomogeneities affect dark-energy precision measurements?
• The luminosity distance-redshift relation up to second order in the Poisson gauge with anisotropic stress
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