Particles of a de Sitter Universe

TL;DR

This paper reviews recent progress in understanding quantum field theory and holography in de Sitter space by analyzing the representations of its isometry group, especially at the late-time boundary.

Contribution

It summarizes advances in how unitary irreducible representations of SO(4,1) manifest in cosmological contexts, enhancing understanding of quantum fields in de Sitter space.

Findings

Representation theory elucidates elementary degrees of freedom in de Sitter.

Manifestations of SO(4,1) representations are observed at the late-time boundary.

Future questions involve boundary and static patch representations.

Abstract

The de Sitter spacetime is a maximally symmetric spacetime. It is one of the vacuum solutions to Einstein equations with a cosmological constant. It is the solution with a positive cosmological constant and describes a universe undergoing accelerated expansion. Among the possible signs for a cosmological constant, this solution is relevant for primordial and late-time cosmology. In the case of zero cosmological constant, studies on the representations of its isometry group have led to a broader understanding of particle physics. The isometry group of $d+1$-dimensional de Sitter is the group $SO(d+1,1)$, whose representations are well known. Given this insight what can we learn about the elementary degrees of freedom in a four dimensional de Sitter universe by exploring how the unitary irreducible representations of $SO(4,1)$ present themselves in cosmological setups? This article aims to summarize recent advances along this line that benefit towards a broader understanding of quantum field theory and holography at different signs of the cosmological constant. Particular focus is given to the manifestation of $SO(4,1)$ representations at the late-time boundary of de Sitter. The discussion is concluded by pointing towards future questions at the late-time boundary and the static patch with a focus on the representations.