Conformal Vacuum of dS${}_4\times \mathbb{R}$ with Oppositely Oriented Boundaries

Abstract

We derive a dS${}_4\times \mathbb{R}$ quotient spacetime that is asymptotically dS${}_4$, where the quotient makes its past boundary oppositely oriented relative to its future boundary. This introduces a lightlike singularity that severs the antipodes of the spacetime and simplifies its global vacuum to a trivial product on antipodal static patches. We show that this state is conformal to the vacuum of an infinite orientable cover of a non-orientable AdS${}_3$ spacetime with an S${}^2$ bundle. The vacuum's separability extends to its holographic dual, which is a product of Cardy states. We find that this candidate dS${}_4$ vacuum state is perturbatively unstable within quantum gravity due to a vanishing Hagedorn temperature.