Fluid and Scalar Field Representations in the Brans–Dicke Theory: Cosmological Scenarios

The Brans–Dicke scalar-tensor cosmological models are studied in both Einstein and Jordan frames, using a hydrodynamical and self-interacting scalar field representations of the energy-momentum tensor leading to the same background solutions. The main features of the corresponding cosmological scenarios are determined. In many cases, the interpolation of decelerating and accelerating regimes are identified. Furthermore, the characteristics of solutions with attractive gravity are analyzed, determining possible implications for Brans–Dicke gravitation theory in the present scenario. The properties of the self-interacting scalar field, including the corresponding potential, are determined. Some possible appealing configurations are identified for the matter content like pressureless $$(\alpha=0)$$ , cosmological constant $$(\alpha={-}1)$$ and phantom matter $$(\alpha={-}2)$$ . The phantom case is motivated by some observational results like those obtained by the DESI project.