Empty space and the (positive) cosmological constant

TL;DR

This paper explores the nature of empty space in relativistic theories and quantum gravity, focusing on the implications of a positive cosmological constant and the choice between de Sitter and elliptic de Sitter spacetimes.

Contribution

It analyzes the relationship between empirical measurements of the cosmological constant and the theoretical representation of empty space in general relativity and quantum gravity.

Findings

Discussion of the role of the cosmological constant in spacetime models

Comparison between de Sitter and elliptic de Sitter spacetimes

Implications for holographic quantum cosmology

Abstract

I discuss empty space, as it appears in the physical foundations of relativistic field theories and in the semiclassical study of isolated systems. Of particular interest is the relationship between empirical measurements of the cosmological constant and the question of appropriate representation of empty space by spacetimes, or models of general relativity. Also considered is a speculative move that shows up in one corner of quantum gravity research. In pursuit of holographic quantum cosmology given a positive cosmological constant, there is evidently some freedom available for theoretical physicists to pick between two physically inequivalent spacetime representations of empty space, moving forward: de Sitter spacetime or its 'elliptic' cousin.