We consider an approach to the Brans-Dicke theory of gravity in which the scalar field has a geometrical nature. By postulating the Palatini variation, we find out that the role played by the scalar field consists in turning the space-time geometry into a Weyl integrable manifold. This procedure leads to a scalar-tensor theory that differs from the original Brans-Dicke theory in many aspects and presents some new features.
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Almeida et al. (2014) studied this question.
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