On the Kinetic Recession Velocities of Astronomical Objects - Ter-Kazarian, G. (Gravitation & cosmology, 2022)
In the framework of the Standard cosmological model, we study the “lookforward” history of the expanding universe, subject to certain rules, in order to calculate the kinetic recession velocity of a luminous source along the line of sight of the observer in a unique way (a coordinate-independent definition), directly from the given cosmological redshift. In this case, we use the method of dividing the cosmological redshift into infinitesimally shifted “relative” spectral intervals between the neighboring emitter and absorber due to expansion of the universe, measured at infinitesimally separated points of space-time, and sum them over to overcome the ambiguity that represents the parallel transport of the four-velocity of the source to the observer in curved Robertson-Walker space-time. In the particular case of such a realization along a null geodesic, we show that the kinetic recession velocity is reduced to the Doppler global velocity. The relationship of the cosmological redshift and the kinetic recession velocity, which is completely different from the formula for the global Doppler shift, leads to important cosmological consequences that the kinetic recession velocity of a galaxy is always subluminal, even for large redshifts of order one or more, and thus it does not violate the fundamental physical principle of causality.