Designer de Sitter Spacetimes

TL;DR

This paper introduces a broad class of solutions called designer de Sitter spacetimes, which are locally similar to de Sitter space but have different global properties, impacting cosmological models.

Contribution

It constructs and analyzes a new family of solutions to Einstein's equations, revealing diverse global dynamics beyond standard de Sitter spacetime.

Findings

Infinite family of locally isometric solutions to de Sitter space

Global dynamics differ significantly from pure de Sitter spacetime

Implications for understanding the universe's structure

Abstract

Recent observations in cosmology indicate an accelerating expansion of the universe postulated to arise from some form of dark energy, the paradigm being positive cosmological constant. De Sitter spacetime is the well-known isotropic solution to the Einstein equations with cosmological constant. However, as discussed here, it is not the most general, locally isotropic solution. One can construct an infinite family of such solutions, designer de Sitter spacetimes, which are everywhere locally isometric to a region of de Sitter spacetime. However, the global dynamics of these designer cosmologies is very different than that of de Sitter spacetime itself. The construction and dynamics of these designer de Sitter spacetimes is detailed along with some comments about their implications for the structure of our universe.