The paper explores a class of $f(R)$ models that accelerate cosmic expansion without a cosmological constant while satisfying both cosmological and solar-system tests in the small-field limit. These models introduce a scalar degree of freedom that, at high curvature, is locked to the general-relativistic prediction, allowing them to pass solar-system tests. However, if cosmological deviations from general relativity are significant, the galactic halo must have a deeper potential than expected in the $\Lambda$CDM model to avoid these tests. The authors argue that the viability of large-deviation models depends on the structure and evolution of the galactic halo, requiring cosmological simulations. They show that even small deviations that satisfy both galactic and solar-system constraints can be detected by future, percent-level measurements of the linear power spectrum. The paper discusses the background evolution, field equations, and linear perturbations of these models, and analyzes local tests of gravity, particularly solar-system constraints, to understand the conditions under which these models can evade local tests of gravity.The paper explores a class of $f(R)$ models that accelerate cosmic expansion without a cosmological constant while satisfying both cosmological and solar-system tests in the small-field limit. These models introduce a scalar degree of freedom that, at high curvature, is locked to the general-relativistic prediction, allowing them to pass solar-system tests. However, if cosmological deviations from general relativity are significant, the galactic halo must have a deeper potential than expected in the $\Lambda$CDM model to avoid these tests. The authors argue that the viability of large-deviation models depends on the structure and evolution of the galactic halo, requiring cosmological simulations. They show that even small deviations that satisfy both galactic and solar-system constraints can be detected by future, percent-level measurements of the linear power spectrum. The paper discusses the background evolution, field equations, and linear perturbations of these models, and analyzes local tests of gravity, particularly solar-system constraints, to understand the conditions under which these models can evade local tests of gravity.