Non-Relativistic Spacetimes with Cosmological Constant

TL;DR

This paper explores how non-relativistic limits of spacetimes with a cosmological constant lead to Newton-Hooke spacetimes, potentially impacting cosmological models and the understanding of the missing-mass problem.

Contribution

It demonstrates the non-relativistic limit of de Sitter spacetimes results in Newton-Hooke spacetimes, revealing modified kinematics relevant to cosmology.

Findings

De Sitter spacetimes reduce to Newton-Hooke spacetimes in the non-relativistic limit.

Non-relativistic kinematics are significantly different from Galilean kinematics.

Potential implications for cosmological models and the missing-mass problem.

Abstract

Recent data on supernovae favor high values of the cosmological constant. Spacetimes with a cosmological constant have non-relativistic kinematics quite different from Galilean kinematics. De Sitter spacetimes, vacuum solutions of Einstein's equations with a cosmological constant, reduce in the non-relativistic limit to Newton-Hooke spacetimes, which are non-metric homogeneous spacetimes with non-vanishing curvature. The whole non-relativistic kinematics would then be modified, with possible consequences to cosmology, and in particular to the missing-mass problem.