Quantum linearization instabilities of de Sitter spacetime. II

For pt.I see ibid., vol.8, no.11, p.1961 (1991). The requirement of de Sitter invariance of physical states in linearized gravity in de Sitter spacetime leads to an apparent paradox. That is, it appears that the vacuum would be the only allowed physical state. The first step toward resolving this paradox is to construct a new Hilbert space of de Sitter-invariant states. First, de Sitter-invariant states with infinite norm are constructed by smearing the states in the original Fock space of linearized gravity over the de Sitter group. Next, a new finite inner product of these states is defined by dividing the original inner product by the infinite volume of the de Sitter group. Then an orthonormal basis for de Sitter-invariant states is given. (The construction of this orthonormal basis provides a proof of the positive-definiteness of the new inner product.) The Hilbert space of de Sitter-invariant states thus obtained is hoped to serve as a starting point towards defining a meaningful perturbative gravity (at the tree level) in de Sitter spacetime.