Longitudinal Doppler effect in de Sitter expanding universe

Abstract

A new redshift formula is obtained considering the longitudinal Doppler effect in the de Sitter expanding universe where the relative geodesic motion is governed by the Lorentzian isometries of our new de Sitter relativity [I. I. Cotăescu, Eur. Phys. J. C 77, 485 (2017)]. This formula combines in a nontrivial manner the well-known cosmological contribution given by Lamaître’s law with that of the relative motion of the source with respect to a fixed observer as in de Sitter relativity instead of special relativity. Other related quantities as the dispersion relation, the propagation time of the photon and the real distance between the source and observer at the moment of observation are discussed pointing out their specific features in the de Sitter relativity.