# Simple kinematic effects on de Sitter expanding universe

## TL;DR

This paper investigates how relativistic effects like time dilation and length contraction manifest in an expanding de Sitter universe, emphasizing their dependence on position and measurement time.

## Contribution

It introduces a framework for analyzing relativistic effects in de Sitter space using conserved quantities and isometries, extending understanding of kinematic phenomena in curved spacetime.

## Key findings

- Time dilation depends on the position and time of measurement.
- Lorentz contraction varies with the location in the expanding universe.
- Relativistic effects are influenced by the universe's expansion and measurement context.

## Abstract

Our recent results concerning the transformation under isometries of the conserved quantities on de Sitter manifolds, allow us to define the rest frame and study the relative geodesic motion in terms of conserved momentum, revealing thus various relativistic effects [I. I. Cotaescu, arXiv:1701.08499]. Here we discuss the time dilation (of the twin paradox) and the Lorentz contraction on the de Sitter expanding portions, pointing out the dependence of these effects on the position and moment in which the time and lengths are measured.