Higher Spin de Sitter Quantum Gravity

TL;DR

This paper investigates how higher spin interactions in de Sitter quantum gravity can render the Euclidean path integral finite, revealing that spin-4 fields are necessary for convergence, unlike just spin-3.

Contribution

It demonstrates that higher spin fields, specifically spin-4, are essential to achieve a finite partition function in de Sitter quantum gravity.

Findings

Higher spins help regularize the Euclidean path integral.

Inclusion of spin-4 fields is necessary for convergence.

Pure Einstein gravity diverges when summing over all saddles.

Abstract

We consider Einstein gravity with positive cosmological constant coupled with higher spin interactions and calculate Euclidean path integral perturbatively. We confine ourselves to the static patch of the 3 dimensional de Sitter space. This geometry, when Euclideanlized is equivalent to 3-sphere. However, infinite number of topological quotients of this space by discrete subgroups of the isometry group are valid Euclidean saddles as well. Pure Einstein gravity is known to diverge, when all saddles are included as contribution to the thermal partition functions (also interpreted as the Hartle Hawking state in the cosmological scenario). We show how higher spins, described by metric-Fronsdal fields help making the partition function finite. Counter-intuitively, this convergence is not achieved by mere inclusion of spin-3, but requires spin-4 interactions.