Odd-dimensional de Sitter Space is Transparent
  We consider quantum field theory in de Sitter space, focusing on the cases of
scalars, spin 1/2 fields, and symmetric and anti-symmetric tensor fields of
arbitrary spin. The free field equations in global coordinates can be reduced
to a one dimensional Schrodinger problem which possesses a remarkable
structure; the potential is of an algebraically special type which appears as a
multi-soliton solution of the KdV equation. In an odd number of spacetime
dimensions these potentials are "transparent" in the sense that their
reflection coefficients vanish identically. This has a remarkable consequence
for physics in de Sitter space. It means that odd dimensional de Sitter space
is transparent in the sense that a quantum state with no particles at past
infinity will evolve into a state with no particles in the far future. This
feature has been previously noted for scalar excitations, but the corresponding
higher spin behaviour (and the proof using algebraic techniques) is new.
