A New Class of Cosmologically `Viable' $f(R)$ Models

Abstract: Instead of assuming a form of gravity and demand cosmology fit with $\Lambda CDM$, a potentially viable' $f(R)$ gravity model is derived assuming an alternative model of cosmology. Taking thedesigner' approach to $f(R)$, a new class of solutions are derived starting with linear coasting cosmology in which scale factor linearly increases with time during matter domination. The derived forms of $f(R)$ are presented as result.