On big crunch solutions in Prokushkin-Vasiliev theory

TL;DR

This paper constructs simple three-dimensional higher spin gravity solutions with matter that model cosmological big crunch scenarios and explores their holographic duals, revealing instability and connections to fermion models.

Contribution

It introduces new solutions in 3D higher spin gravity with matter, including twisted sectors and a parameter for scalar mass variation, advancing holographic cosmology models.

Findings

Solutions describe bubble growth ending in big crunch

Evidence of dual field theory instability via multi-trace deformation

The $ ext{lambda} o 0$ limit relates to large-N fermion models

Abstract

We construct simple solutions of three-dimensional higher spin gravity interacting with matter in which only the scalar and spin-two fields are excited. They preserve Lorentz symmetry and are similar to the four-dimensional solutions constructed by Sezgin and Sundell, with the difference that the additional twisted sectors of the three-dimensional theory are excited. Furthermore, the three-dimensional system contains an extra parameter $\lambda$ which allows us to vary the mass of the scalar. Among other reasons, the resulting solutions are interesting for the holographic study of cosmological singularities: they describe the growth of a Coleman-De Luccia bubble in anti-de Sitter space, ending in a big crunch singularity. We initiate the holographic study of these solutions, finding evidence for their interpretation within a multi-trace deformation which renders the dual field theory unstable. The limit $\lambda \to 0$ is particularly interesting as it captures effects of a running coupling in a large-$N$ interacting fermion model. We also propose a generalization of our solutions, consisting of a dressing with Lorentz-invariant projectors. This additional sector remains non-trivial when the scalar field is turned off.