Abstract
Nojiri \& Odintsov \cite{noj1} and Hu \& Sawicki \cite{hu} have studied non-linear functions in modified gravity that explain the cosmic acceleration without cosmological constant, fulfil the conditions of local gravity \& stability and pass the solar system tests. In this paper, FRW model, a best fitted and fruitful mathematical model of the physical universe \cite{rob, hub, alph, pen} is studied in the context of these non-linear functions. The cosmological implications such as Hubble parameter, deceleration parameter, jerk parameter, matter density and the effective equation of state parameter of the universe are plotted with respect to redshift. Subsequently, the age of the universe is predicted in $f(R)$ gravity. All are found to represent the features of present phase of the universe.
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