The inflationary scenario in the $f(R)$ gravity model with a $R^4$ term

We investigate the cosmic inflation scenario of a specific $f(R)$ model that contains more than one higher-order term in $R$. The $f(R)$ considered here has the terms $R^2$, $R^3$, and $R^4$ along with the linear term. A rigorous investigation has been carried out in the presence of these higher-order terms to figure out whether it leads to a physically sensible cosmic inflationary model. We examine in detail, subject to which conditions this $f(R)$ model renders a viable inflationary scenario, and it has been found that the outcomes of our study agree well with the recent PLANCK results.