Abstract
In this thesis we constrain the designer f(R) models by the observations in both cosmological and local scales. For the cosmological observation constraints, we find that although the designer f(R) can generate any desired cosmic expansion his-tory, it suffers from the fine-tuning problem in order to fit the large scale structure constraints well. For local gravity constraints, so far we do search out the viable designer f(R) models that can satisfy the local gravity constraints but would be indistinguishable from the ΛCDM model even considering the observations in both cosmological and local scales and for other effective equation of states we consider in this thesis, we do not find out any viable designer f(R) model.
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