Delicate f(R) gravity models with a disappearing cosmological constant and observational constraints on the model parameters

We study the f(R) theory of gravity using the metric approach. In particular we investigate the recently proposed model by Hu and Sawicki; Appleby and Battye; and Starobinsky. In this model, the cosmological constant is zero in flat space time. The model passes both the solar system and the laboratory tests. But the model parameters need to be fine-tuned to avoid the finite time singularity recently pointed to in the literature. We check the concordance of this model with the H(z) and baryon acoustic oscillation data. We find that the model resembles the Lambda CDM at high redshift. However, for some parameter values there are variations in the expansion history of the universe at low redshift.