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The process of minimal extension of a scalar-metric theory to a scalar-metric-torsion gravitational theory, by replacing the Levi-Civita connection by a general affine connection with torsion, is shown to be nonunique. Additional parameters, in addition to the usual Brans-Dicke parameter ω, may enter the theory unless physical principals are introduced to constrain their appearance.
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Larry L. Smalley (1978) studied this question.
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