Horizon Complimentarity in Elliptic de Sitter Space

Primordial Universe and Gravity (PUG) Discussions, Pennsylvania State University

Elliptic de Sitter space is regular de Sitter space in which one identifies antipodal points. The resulting spacetime is not time-orientable, but it also does not contain any closed timelike curves. Classically, a single observer is unable to distinguish it from regular de Sitter and it that sense it is not less real than regular de Sitter spacetime. Every observer finds cosmological horizons, but due to the antipodal identification there is nothing behind new behind the horizon. This realizes horizon complimentarity – the idea that on both sides of the horizon the full information about the world should be encoded. In this talk, I will give a quick introduction to elliptic de Sitter space. After this I will define a classical scalar field theory and explain why there is no classical phasespace with a symplectic form implying that there does not exist a global Hilbert space of its quantum theory. Finally, I will present a framework introducing observer dependent Hilbert spaces together with translation recipes for states and operators.