Can structure formation distinguish \Lambda CDM from non-minimal f(R)
  Gravity?
  Non-minimally 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 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 non-minimally coupled to the matter lagrangian) that
produces the similar background cosmology as in \Lambda CDM. Subsequently we
calculate the growth for the matter over density g(z) for such non minimally
coupled f(R) models and compare them with the \Lambda 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 non-minimally
coupled f(R) gravity models as well as for the \Lambda CDM. Our results show
that there is a small but finite window where one can distinguish the
non-minimally coupled f(R) models with the concordance \Lambda CDM.
