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.

中文翻译：

---

德西特膨胀宇宙中的纵向多普勒效应

考虑到德西特膨胀宇宙中的纵向多普勒效应，获得了一个新的红移公式，其中相对测地线运动由我们新的德西特相对论的洛伦兹等距控制 [II Cotăescu, Eur. 物理。J. C 77, 485 (2017)]。这个公式以非平凡的方式结合了拉迈特定律给出的众所周知的宇宙学贡献与源相对于固定观察者的相对运动的贡献，例如在德西特相对论而不是狭义相对论中。其他相关量如色散关系、光子的传播时间和观察时刻源与观察者之间的实际距离等，指出了它们在德西特相对论中的具体特征。