Obstacles to Constructing de Sitter Space in String Theory

TL;DR

This paper discusses the difficulties and limitations in constructing de Sitter space within string theory, highlighting the challenges in current approximations and the implications for the de Sitter swampland conjecture.

Contribution

It clarifies that current controlled approximations in string theory are insufficient to definitively construct or rule out de Sitter space, supporting the swampland conjecture.

Findings

Controlled approximations require small parameters with severe constraints

Understanding of big-bang and big-crunch singularities is lacking

The existence of metastable de Sitter space remains conjectural

Abstract

There have been many attempts to construct de Sitter space-times in string theory. While arguably there have been some successes, this has proven challenging, leading to the de Sitter swampland conjecture: quantum theories of gravity do not admit stable or metastable de Sitter space. Here we explain that, within controlled approximations, one lacks the tools to construct de Sitter space in string theory. Such approximations would require the existence of a set of (arbitrarily) small parameters, subject to severe constraints. But beyond this one also needs an understanding of big-bang and big-crunch singularities that is not currently accessible to standard approximations in string theory. The existence or non-existence of metastable de Sitter space in string theory remains a matter of conjecture.