On Principle of Inertia in Closed Universe

TL;DR

This paper explores the principle of inertia in a closed universe with de Sitter asymptotics, proposing that gravity should be locally invariant under de Sitter transformations, offering a new perspective on cosmological inertia.

Contribution

It introduces a framework where the universe's asymptotic behavior and inertia principles are linked through de Sitter space, challenging traditional Einsteinian gravity.

Findings

Universe likely closed with curvature related to the cosmological constant

Inertia systems can be fixed in de Sitter space without circular reasoning

Gravity should be locally invariant under de Sitter transformations

Abstract

If our universe is asymptotic to a de Sitter space, it should be closed with curvature in $O(\Lambda)$ in view of dS special relativity. Conversely, its evolution can fix on Beltrami systems of inertia in the dS-space without Einstein's `argument in a circle'. Gravity should be local dS-invariant based on localization of the principle of inertia.