Longitudinal Doppler effect in de Sitter expanding universe

TL;DR

This paper derives a new redshift formula considering the longitudinal Doppler effect within the de Sitter expanding universe, integrating cosmological and relativistic effects unique to de Sitter relativity.

Contribution

It introduces a novel redshift formula that combines cosmological and relativistic effects in de Sitter relativity, extending previous models.

Findings

New redshift formula incorporating de Sitter relativity effects

Analysis of photon propagation time and source-observer distance in this framework

Discussion of dispersion relation and related quantities in de Sitter 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 Lorenzian isometries of our new de Sitter relativity [I. I. Cot\u aescu, {Eur. Phys. J. C} {\bf 77} (2017) 485]. This formula combines in a non-trivial manner the well-known cosmological contribution given by Lama\' itre'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 source and observer at the moment of observation are discussed pointing out their specific features in the de Sitter relativity.