FRW and domain walls in higher spin gravity

TL;DR

This paper constructs exact solutions in four-dimensional higher spin gravity that resemble cosmological and domain wall backgrounds, using twistor space methods, and explores their implications in holography and perturbation theory.

Contribution

It introduces a holomorphic factorization method in twistor space to find exact higher spin solutions with cosmological and domain wall interpretations, extending the understanding of higher spin backgrounds.

Findings

Exact solutions with FRW and domain wall geometries in higher spin gravity.

Higher spin symmetry extensions of spacetime isometries with infinite-dimensional algebras.

Perturbation theory around these solutions suggests black hole-like states for nonlinear completion.

Abstract

We present exact solutions to Vasiliev's bosonic higher spin gravity equations in four dimensions with positive and negative cosmological constant that admit an interpretation in terms of domain walls, quasi-instantons and Friedman-Robertson-Walker (FRW) backgrounds. Their isometry algebras are infinite dimensional higher-spin extensions of spacetime isometries generated by six Killing vectors. The solutions presented are obtained by using a method of holomorphic factorization in noncommutative twistor space and gauge functions. In interpreting the solutions in terms of Fronsdal-type fields in spacetime, a field-dependent higher spin transformation is required, which is implemented at leading order. To this order, the scalar field solves Klein-Gordon equation with conformal mass in (anti) de Sitter space. We interpret the FRW solution with de Sitter asymptotics in the context of inflationary cosmology and we expect that the domain wall and FRW solutions are associated with spontaneously broken scaling symmetries in their holographic description. We observe that the factorization method provides a convenient framework for setting up a perturbation theory around the exact solutions, and we propose that the nonlinear completion of particle excitations over FRW and domain wall solutions requires black hole-like states.