Study of a quadratic redshift-based correction in f(R) gravity with Baryonic matter

This paper is considered as a second-order redshift-based corrections in derivative of modified gravitational action, f(R), to explain the late time acceleration which is appeared by Supernova Type Ia (SNeIa) without considering the dark components. Here, we obtained the cosmological dynamic parameters of universe for this redshift depended corrections. Next, we used the recent data of SNeIa Union2, shift parameter of the cosmic background radiation, Baryon acoustic oscillation from sloan digital sky survey (SDSS), and combined analysis of these observations to put constraints on the parameters of the selected F(z) model. It is very interesting that the well-known age problem of the three old objects for combined observations can be alleviated in this model. Finally, the reference action will be constructed in terms of its Taylor expansion. Also, we show that the reconstructed action definitely pass the solar system and stability of the cosmological solution tests.