Abstract
In de Sitter space, the theory of the conformal factor of quantum gravity becomes nontrivial when corrections from quantum matter fields are considered. In the corresponding theory there appear five zero modes associated with five-dimensional gauge invariance. We quantize a toy model which possesses that same property. The construction of the states of the theory is unusual: indeed, the ground state is a de Sitter-invariant but unnormalizable state; moreover, the space of states is a superposition of Fock spaces, each of which contains a vacuum which breaks de Sitter invariance. We then argue that quantum gravity must spontaneously break the O(1,4) symmetry group of the gravitational background. This could provide a simple dynamical solution to the cosmological-constant problem.
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