Analytic extensions of Starobinsky model of inflation

We study several extensions of the Starobinsky model inflation, which obey all observational constraints on inflationary parameters, by demanding that both inflaton scalar potential in Einstein frame and $F(R)$ gravity function Jordan have explicit dependence upon fields {\it and} parameters terms elementary functions. Our models are continuously connected to original via changing parameters. modify $(R+R^2)$ adding an $R^3$-term, $R^4$-term, $R^{3/2}$-term, respectively, calculate potentials, observables allowed limits deformation using latest bounds. find tensor-to-scalar ratio modified $R^{3/2}$-term significantly increases with raising parameter front term. On other side, we deform powers $y=\exp\left(-\sqrt{\frac{2}{3}}\phi/M_{Pl}\right)$, where $\phi$ is canonical (scalaron) field, corresponding functions two new cases, restrictions lowest orders respect variable $y$ physically small during slow-roll inflation.