More hilltop inflation models

Using analytic expressions, we explore the parameter space for hilltop inflation models with a potential of the form $V_0\pm m^2{\varphi }^2-a{\varphi }^p$. With the positive sign and p>2 this converts the original hybrid inflation model into a hilltop model, allowing the spectral index to agree with the observed value n=0.95. In some cases the observed value is theoretically favored, while in others there is only the generic prediction $\mathrm{\mid }n-1\mathrm{\mid }\text{lsim}1$.