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

Fanizza, G.; Marozzi, G.; Gasperini, M.; Veneziano, G.

doi:10.1016/j.physletb.2016.04.032

Article
Report number	arXiv:1512.08489 ; CERN-PH-TH-2015-306 ; CERN-PH-TH-2015-306
Title	Time of flight of ultra-relativistic particles in a realistic Universe: a viable tool for fundamental physics?
Author(s)	Fanizza, G. (Geneva U., CAP ; Bari U. ; Geneva U., Dept. Theor. Phys. ; INFN, Bari) ; Gasperini, M. (Bari U. ; INFN, Bari) ; Marozzi, G. (Rio de Janeiro, CBPF ; Geneva U., CAP ; Geneva U., Dept. Theor. Phys.) ; Veneziano, G. (College de France ; CERN ; Rome U.)
Publication	2016-06-10
Imprint	28 Dec 2015
Number of pages	5
Note	6 pages, 2 figures, Typos corrected, clarifications and a reference added. Version accepted for publication in Physics Letter B
In:	Phys. Lett. B 757 (2016) 505-509
DOI	10.1016/j.physletb.2016.04.032
Subject category	Astrophysics and Astronomy
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 gauge 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.
Copyright/License	arXiv nonexclusive-distrib. 1.0 publication: © 2016-2025 The Author(s) (License: CC-BY-4.0), sponsored by SCOAP³ preprint: © 2015-2025 CERN (License: CC-BY-4.0)

$Expected fractional dispersion of measurements of flight-time differences of UR particles, according to Eq. (\ref{dispersion}), as induced by a realistic spectrum of fluctuations in the CDM (dotted curve) and $\La$CDM (dashed curve) case. We also plot the fractional dispersion $\widehat\sg$ defined in Eq. (\ref{23}) and associated with the present experimental uncertainty on the value of the cosmological constant (solid curve).$ $Same as Fig. 1 for the range $0.01 < z_s < 0.1$. The dispersion $\widehat\sg$ (not shown) is negligibly small in this range.$