On Special Relativity with Cosmological Constant

TL;DR

This paper extends special relativity to include a cosmological constant, proposing a new framework based on Beltrami-de Sitter spacetime that links local physics with cosmological observations.

Contribution

It introduces a modified special relativity theory incorporating the cosmological constant using Beltrami-de Sitter spacetime, defining new observables and simultaneity concepts.

Findings

Predicts positive spatial curvature of the universe.

Generalizes Einstein's mass-energy relation.

Links special relativity with cosmological principles.

Abstract

Based on the principle of relativity and the postulate of invariant speed and length, we propose the theory of special relativity with cosmological constant ${\cal SR}_{c,R}$ if the invariant length whose square is the inverse of the one-third cosmological constant of the universe. It is on the Beltrami-de Sitter spacetime ${\cal B}_R$ with de Sitter invariance. We define the observables of free particles and generalize famous Einstein's formula. We also define two kinds of simultaneity. The first is for local experiments and inertial motions. The second is for cosmological observations. Thus there is a relation between the relativity principle and the cosmological principle. We predict that the 3-d cosmic space is then of positive spatial curvature of order cosmological constant. The relation between ${\cal SR}_{c,R}$ and the doubly special relativity is briefly disucssed.