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

Instead of assuming a form of gravity and demand cosmology fit with $\Lambda CDM$,apotentially\mathrm{‘}viabl{e}^{\mathrm{\prime }}$f®$ gravity model is derived assuming an alternative model of cosmology. Taking the `designer’ 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.