Novel scalar degrees of freedom emerging from hybrid metric-Palatini gravity

TL;DR

The paper develops a generalized Hybrid Metric–Palatini Scalar–Tensor (HMPST) theory that couples a Brans–Dicke–like field $\phi$ to a Palatini-type curvature through a function $f(\hat{R})$, producing two dynamical scalar degrees of freedom. Focusing on the analytically tractable linear-$f(\hat{R})$ subclass, it derives cosmological solutions including de Sitter and matter-dominated phases, and constructs static, spherically symmetric vacuum spacetimes that generalize the Janis–Newman–Winicour and Buchdahl metrics, with Schwarzschild–de Sitter limits. In the weak-field regime, linear perturbations yield Yukawa-type corrections to the Newtonian potential with an effective $G_{\rm eff}$ and post-Newtonian parameter $\gamma$, recovering GR for heavy or weakly coupled scalars. The results demonstrate a unified gravity description across cosmological, astrophysical, and Solar System scales and highlight the potential of HMPST as a bridge between modified gravity and EFT-inspired extensions.

Abstract

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 $φ$ modulates the curvature couplings, enriching the dynamics and enabling nontrivial self-interactions through scalar potentials. We focus on the analytically tractable linear-$f(\hat{R})$ 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 $G_{\rm eff}$ and post-Newtonian parameter $γ$ that recover General Relativity for heavy or weakly coupled scalars. These results show that the linear-$f(\hat{R})$ 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.