Massless Minimally Coupled Fields in De Sitter Space: O(4)-Symmetric States Versus De Sitter Invariant Vacuum

The issue of de Sitter invariance for a massless minimally coupled scalar field is revisited. Formally, it is possible to construct a de Sitter invariant state for this case provided that the zero mode of the field is quantized properly. Here we take the point of view that this state is physically acceptable, in the sense that physical observables can be computed and have a reasonable interpretation. In particular, we use this vacuum to derive a new result: that the squared difference between the field at two points along a geodesic observer's space-time path grows linearly with the observer's proper time for a quantum state that does not break de Sitter invariance. Also, we use the Hadamard formalism to compute the renormalized expectation value of the energy momentum tensor, both in the O(4) invariant states introduced by Allen and Follaci, and in the de Sitter invariant vacuum. We find that the vacuum energy density in the O(4) invariant case is larger than in the de Sitter invariant case.