Janus Deformation of de Sitter Space and Transitions in Gravitational Algebras

We consider a time-dependent $\mathcal{O}(1/G)$ deformation of pure de Sitter (dS) space in dS gravity coupled to a massless scalar field. It is the dS counterpart of the AdS Janus deformation and interpolates two asymptotically dS spaces in the far past and the far future with a single deformation parameter. The Penrose diagram can be elongated along the time direction indefinitely as the deformation becomes large. After studying the classical properties of the geometry such as the area theorem and the fluctuation by a matter field, we explore the algebraic structure of the field operators on the deformed spacetime. We argue that the algebra is a von Neumann factor of type II$_\infty$ for small deformations, but there occurs a transition to type I$_\infty$ as the deformation increases so that the neck region of the deformed space becomes a Lorentzian cylinder.
Comment: 1+19 pages, 3 figures v2: added references