The nonminimally coupled $f(R)$ gravity model is an interesting approach to explain the late time acceleration of the Universe without introducing any exotic matter component in the energy budget of the Universe. But distinguishing such model with the concordance $\Lambda$ cold dark matter $(\Lambda \mathrm{CDM})$ model using present observational data is a serious challenge. In this paper, we address this issue using the observations related to the growth of matter over density $g(z)$ as measured by different galaxy surveys. As background cosmology is not sufficient to distinguish different dark energy models, we first find out the functional form for $f(R)$ (which is nonminimally coupled to the matter Lagrangian) that produces the similar background cosmology as in $\Lambda \mathrm{CDM}$. Subsequently we calculate the growth for the matter over density $g(z)$ for such nonminimally coupled $f(R)$ models and compare them with the $\Lambda \mathrm{CDM}$ universe. We also use the measurements of $g(z){\sigma }_8(z)$ by different galaxy surveys to reconstruct the behavior for $g(z)$ and ${\sigma }_8(z)$ for both the nonminimally coupled $f(R)$ gravity models as well as for the $\Lambda \mathrm{CDM}$. Our results show that there is a small but finite window where one can distinguish the nonminimally coupled $f(R)$ models with the concordance $\Lambda \mathrm{CDM}$.

• Received 7 June 2013

DOI:https://doi.org/10.1103/PhysRevD.88.044043