On the kinematic interpretation of cosmological redshifts

Abstract

We describe what is essentially a correct solution to the kinematic interpretation of cosmological redshifts in standard cosmological model. In the framework of "stretching of space" point of view of the spatially homogeneous and isotropic Robertson-Walker space-time of standard cosmological model, we study so-called "lookforward" history of expanding universe, subject to certain rules, in order to overcome the ambiguity of the parallel transport of source four-velocity along the null geodesic to an observer. We interpret the cosmological redshifts as the accumulation of a series of infinitesimal "relative" spectral shifts along the path of light consequent on recession. The crux of our solution is the kinetic recession velocity of comoving astronomical object, which is always subluminal even for large redshifts of order one or more, so that it does not violate the fundamental physical principle of causality. Our analysis establishes a straightforward kinematic relationship of overall cosmological redshift and kinetic recession velocity, which is utterly distinct from a familiar global Doppler shift formula. A difference of global Doppler velocity and kinetic recession velocity, for redshifts 0.9 ≤ z ≤ 800, is ≥ 0.072c, where a maximum value, 0.187c, is reached at redshifts z = 4.5 - 5.1. A general solution is reduced to a global Doppler shift along the null geodesic. We discuss the implications for the case of a zero-density cosmological model of Milne universe, whereas a correspondence to the more usual special relativity notion of relative speed retains. In Table 1, we are summing up kinetic recession velocities of some typical distant astronomical objects with spectroscopic redshift determinations collected from the literature.

Relative velocity in pseudo-Riemannian spacetime

“…For a benefit of the reader, in this section we necessarily revisit a general solution for relative velocity of luminous source, an early version of which is given in (Ter-Kazarian, 2021b). In this section much more will be done to make the early results and formulations clear and rigorous, which are in use throughout the present paper.…”