This paper proposes a class of $ f(R) $ gravity models that produce a viable cosmology different from the LambdaCDM model, satisfying cosmological, solar system, and laboratory tests. These models have flat and de Sitter spacetimes as solutions in the absence of matter. The cosmological constant is zero in flat space but appears effectively in curved space for large R. A key feature is the "disappearing cosmological constant," where the effective cosmological constant disappears in flat space but reappears in curved space. The model predicts a small discrepancy in the slope of the primordial perturbation power spectrum from galaxy surveys and CMB fluctuations. However, it also raises a new problem: overproduction of scalarons (massive scalar particles) in the early universe. The model is based on a 3-parametric form of $ f(R) $, which allows for a regular $ f(R) $ satisfying $ f(0) = 0 $, meaning no bare cosmological constant in flat space. The model passes laboratory and solar system tests if the parameter $ n $ is sufficiently large (at least 2). However, the model faces challenges in avoiding overproduction of scalarons, which could lead to a weak singularity. The model also shows that the growth of linear perturbations at recent redshifts imposes a stronger limit on $ n $, leading to a discrepancy in the slope of the primordial power spectrum between galaxy surveys and CMB data. This discrepancy could serve as a strong argument for the model. The paper concludes that while the model is viable, further study is needed to address the issue of scalaron overproduction and to refine the constraints on $ n $.This paper proposes a class of $ f(R) $ gravity models that produce a viable cosmology different from the LambdaCDM model, satisfying cosmological, solar system, and laboratory tests. These models have flat and de Sitter spacetimes as solutions in the absence of matter. The cosmological constant is zero in flat space but appears effectively in curved space for large R. A key feature is the "disappearing cosmological constant," where the effective cosmological constant disappears in flat space but reappears in curved space. The model predicts a small discrepancy in the slope of the primordial perturbation power spectrum from galaxy surveys and CMB fluctuations. However, it also raises a new problem: overproduction of scalarons (massive scalar particles) in the early universe. The model is based on a 3-parametric form of $ f(R) $, which allows for a regular $ f(R) $ satisfying $ f(0) = 0 $, meaning no bare cosmological constant in flat space. The model passes laboratory and solar system tests if the parameter $ n $ is sufficiently large (at least 2). However, the model faces challenges in avoiding overproduction of scalarons, which could lead to a weak singularity. The model also shows that the growth of linear perturbations at recent redshifts imposes a stronger limit on $ n $, leading to a discrepancy in the slope of the primordial power spectrum between galaxy surveys and CMB data. This discrepancy could serve as a strong argument for the model. The paper concludes that while the model is viable, further study is needed to address the issue of scalaron overproduction and to refine the constraints on $ n $.