We study a class of metric-variation f(R) models that accelerate the expansion without a cosmological constant and satisfy both cosmological and solar-system tests in the small-field limit of the parameter space. Solar-system tests alone place only weak bounds on these models, since the additional scalar degree of freedom is locked to the high-curvature general-relativistic prediction across more than 25 orders of magnitude in density, out through the solar corona. This agreement requires that the galactic halo be of sufficient extent to maintain the galaxy at high curvature in the presence of the low-curvature cosmological background. If the galactic halo and local environment in f(R) models do not have substantially deeper potentials than expected in ΛCDM, then cosmological field amplitudes |f_R| ≳ 10⁻⁶ will cause the galactic interior to evolve to low curvature during the acceleration epoch. Viability of large-deviation models therefore rests on the structure and evolution of the galactic halo, requiring cosmological simulations of f(R) models, and not directly on solar-system tests. Even small deviations that conservatively satisfy both galactic and solar-system constraints can still be tested by future, percent-level measurements of the linear power spectrum, while they remain undetectable to cosmological-distance measures. Although we illustrate these effects in a specific class of models, the requirements on f(R) are phrased in a nearly model-independent manner. The paper discusses the cosmological impact of f(R) models of the acceleration. It introduces a class of models that accelerate the expansion without a true cosmological constant but nonetheless includes the phenomenology of ΛCDM as a limiting case. The paper then describes the background equations of motion and their representation as an equation for the scalar degree of freedom. It calculates the expansion history and linear power spectrum in the class of f(R) models. The paper also analyzes local tests of gravity and shows that solar-system tests alone are fairly easy to evade, provided gravity behaves similarly to general relativity in the galaxy. However, if cosmological deviations from general relativity are required to be large, the latter condition is satisfied only with extreme and testable changes to the galactic halo. The paper discusses these results in detail. The paper also discusses the local tests of f(R) gravity. It considers the general metric around spherically symmetric sources and its relationship to the f_R field. It discusses the qualitative behavior of the field solutions and their relationship with the Compton wavelength. It evaluates solar-system constraints and the requirements they place on the extent and evolution of the galactic halo. The paper shows that the Compton condition is satisfied for the whole solar profile for |f_R0| ≲ 10⁻². The thin-shell criterion is satisfied in the solar corona up to |f_R0| ≲ 10⁻¹. Thus, for n = 4, we expect order-unity cosmWe study a class of metric-variation f(R) models that accelerate the expansion without a cosmological constant and satisfy both cosmological and solar-system tests in the small-field limit of the parameter space. Solar-system tests alone place only weak bounds on these models, since the additional scalar degree of freedom is locked to the high-curvature general-relativistic prediction across more than 25 orders of magnitude in density, out through the solar corona. This agreement requires that the galactic halo be of sufficient extent to maintain the galaxy at high curvature in the presence of the low-curvature cosmological background. If the galactic halo and local environment in f(R) models do not have substantially deeper potentials than expected in ΛCDM, then cosmological field amplitudes |f_R| ≳ 10⁻⁶ will cause the galactic interior to evolve to low curvature during the acceleration epoch. Viability of large-deviation models therefore rests on the structure and evolution of the galactic halo, requiring cosmological simulations of f(R) models, and not directly on solar-system tests. Even small deviations that conservatively satisfy both galactic and solar-system constraints can still be tested by future, percent-level measurements of the linear power spectrum, while they remain undetectable to cosmological-distance measures. Although we illustrate these effects in a specific class of models, the requirements on f(R) are phrased in a nearly model-independent manner. The paper discusses the cosmological impact of f(R) models of the acceleration. It introduces a class of models that accelerate the expansion without a true cosmological constant but nonetheless includes the phenomenology of ΛCDM as a limiting case. The paper then describes the background equations of motion and their representation as an equation for the scalar degree of freedom. It calculates the expansion history and linear power spectrum in the class of f(R) models. The paper also analyzes local tests of gravity and shows that solar-system tests alone are fairly easy to evade, provided gravity behaves similarly to general relativity in the galaxy. However, if cosmological deviations from general relativity are required to be large, the latter condition is satisfied only with extreme and testable changes to the galactic halo. The paper discusses these results in detail. The paper also discusses the local tests of f(R) gravity. It considers the general metric around spherically symmetric sources and its relationship to the f_R field. It discusses the qualitative behavior of the field solutions and their relationship with the Compton wavelength. It evaluates solar-system constraints and the requirements they place on the extent and evolution of the galactic halo. The paper shows that the Compton condition is satisfied for the whole solar profile for |f_R0| ≲ 10⁻². The thin-shell criterion is satisfied in the solar corona up to |f_R0| ≲ 10⁻¹. Thus, for n = 4, we expect order-unity cosm