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

TL;DR

This paper introduces an extended hybrid metric-Palatini scalar-tensor gravity theory with an additional scalar field, analyzing its cosmological, strong-field, and weak-field solutions, and demonstrating its consistency with observations across scales.

Contribution

It develops the hybrid metric-Palatini scalar-tensor theory with an extra scalar field, providing analytic solutions and showing its viability from cosmological to Solar System scales.

Findings

Identifies de Sitter and matter-dominated cosmological solutions.

Derives static spherically symmetric solutions generalizing known metrics.

Finds Yukawa-type corrections to gravity in the weak-field regime.

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 $\phi$ 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 $\gamma$ 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.