Scalar-connection gravity and spontaneous scalarization

Scalar-tensor theories of gravity are known to allow significant deviations from general relativity through various astrophysical phenomena. In this paper, we formulate a scalar-connection by setting up scalars and connection configurations instead metric. Since the matter sector is not straightforward conceive without metric, invoke cosmological fluids in terms their one-form velocity volume element invariant action. This leads gravitational equations with perfect fluid source generated which expected produce reasonable strong field regime. As relevant application, study spontaneous scalarization mechanism show that Damour-Esposito-Far\`ese model arises certain class gravity. Furthermore, investigate present framework becomes distinguishable famed scalar-tensor theories.