Hybrid metric-Palatini gravity unifies the metric and Palatini formalisms while preserving a propagating scalar degree of freedom, offering a compelling route to modified gravity consistent with current observations. Motivated by this success, we consider an extended framework—the hybrid metric-Palatini scalar-tensor (HMPST) theory—in which an additional scalar field $\varphi$ modulates the curvature couplings, enriching the dynamics and enabling nontrivial self-interactions through scalar potentials. We focus on the analytically tractable linear-$f(\widehat{R})$ subclass and study its cosmological, strong-field, and weak-field regimes. In homogeneous and isotropic settings, we identify de Sitter and matter-dominated cosmological solutions describing accelerated expansion and early-Universe behavior. For static, spherically symmetric configurations, the field equations yield analytic solutions generalizing the Janis-Newman-Winicour and Buchdahl metrics, including the Schwarzschild–de Sitter limit. In the weak-field regime, linearized perturbations around Minkowski space lead to Yukawa-type corrections to the gravitational potential, with an effective Newton constant $G_{\mathrm{eff}}$ and post-Newtonian parameter $\gamma$ that recover general relativity for heavy or weakly coupled scalars. These results show that the linear-$f(\widehat{R})$ HMPST subclass provides a consistent and unified description of gravity across cosmological, astrophysical, and Solar System scales, offering a fertile framework for connecting modified gravity to observations and effective field-theoretic extensions.

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• Alternative gravity theories
• General relativity