We reconstruct an f(R) gravity model that gives rise to the particular $\Lambda \mathrm{CDM}$ background evolution of the Universe. We find well-defined, real-valued analytical forms for the f(R) model to describe the Universe both in the early epoch from the radiation to matter dominated eras and the late time acceleration period. We further examine the viability of the derived f(R) model and find that it is viable to describe the evolution of the Universe in the past and the future singularity does not exist in the Lagrangian.

• Received 16 August 2012

DOI:https://doi.org/10.1103/PhysRevD.87.023508