# de Sitter invariant special relativity and galaxy rotation curves

## TL;DR

This paper proposes a de Sitter invariant special relativity framework that modifies Newtonian gravity, potentially explaining galaxy rotation curves without dark matter by incorporating invariant length scales at the Planck level.

## Contribution

It introduces a de Sitter invariant special relativity and derives a modified Newtonian force that can account for galaxy rotation curves without dark matter.

## Key findings

- Modified Newtonian force explains galaxy rotation curves.
- De Sitter invariance alters relativistic theories.
- Potential to eliminate need for dark matter in galactic dynamics.

## Abstract

Owing to the existence of an invariant length at the Planck scale, Einstein special relativity breaks down at that scale. A possible solution to this problem is arguably to replace the Poincar\'e invariant Einstein special relativity by a de Sitter invariant special relativity. In addition to reconciling Lorentz symmetry with the existence of an invariant length, such replacement produces concomitant changes in all relativistic theories, including general relativity, which becomes what we have called 'de Sitter modified general relativity'. In this paper, the Newtonian limit of this theory is used to study the circular velocity of stars around the galactic center. It is shown that the de Sitter modified Newtonian force---which includes corrections coming from the underlying local kinematics---could possibly explain the rotation curve of galaxies without the necessity of supposing the existence of a dark matter halo.