A Euclidean lattice formulation is presented of the general fourth-order gravitational action involving R_μν² terms. This lattice theory is bounded and reflection positive. The existence of a positive Hilbert space and Hamiltonian, and hence unitarity, follow then from the standard nonperturbative Osterwalder-Schrader construction.
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E. T. Tomboulis (1984) studied this question.
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