An exact solution of 4D higher-spin gauge theory

Abstract

We give a one-parameter family of exact solutions to 4D higher-spin gauge theory invariant under a deformed higher-spin extension of SO ( 3 , 1 ) and parameterized by a zero-form invariant. All higher-spin gauge fields vanish, while the metric interpolates between two asymptotically AdS 4 regions via two dS 3 -foliated domain walls and two H 3 -foliated Robertson–Walker spacetimes—one in the future and one in the past—with the scalar field playing the role of foliation parameter. All Weyl tensors vanish, including that of spin two. We furthermore discuss methods for constructing solutions, including deformation of solutions to pure AdS gravity, the gauge-function approach, the perturbative treatment of (pseudo-)singular initial data describing isometric or otherwise projected solutions, and zero-form invariants.