  Recent arguments have indicated that the sum over histories formulation of
quantum amplitudes for gravity should include sums over conifolds, a set of
histories with more general topology than that of manifolds. This paper
addresses the consequences of conifold histories in gravitational functional
integrals that also include scalar fields. This study will be carried out
explicitly for the generalized Hartle-Hawking initial state, that is the
Hartle-Hawking initial state generalized to a sum over conifolds. In the
perturbative limit of the semiclassical approximation to the generalized
Hartle-Hawking state, one finds that quantum field theory on Einstein conifolds
is recovered. In particular, the quantum field theory of a scalar field on de
Sitter spacetime with $RP^3$ spatial topology is derived from the generalized
Hartle-Hawking initial state in this approximation. This derivation is carried
out for a scalar field of arbitrary mass and scalar curvature coupling.
Additionally, the generalized Hartle-Hawking boundary condition produces a
state that is not identical to but corresponds to the Bunch-Davies vacuum on
$RP^3$ de Sitter spacetime. This result cannot be obtained from the original
Hartle-Hawking state formulated as a sum over manifolds as there is no Einstein
manifold with round $RP^3$ boundary.
