Testing $f(R)$ dark energy model with the large scale structure

In this work, we further investigate the family of $f(R)$ dark energy models that can exactly mimic the same background expansion history as that of the $\mathrm{\Lambda }$CDM model. We study the large scale structure in the $f(R)$ gravity using the full set cosmological perturbation equations. We investigate the structure formation in both the spatially flat and curved Universe. We also confront our model with the latest observations and conduct a Markov Chain Monte Carlo analysis on the parameter space.