On hilltop and brane inflation after Planck

Abstract

Hilltop inflation models are often described by potentials $V=V_0(1-\frac{{\varphi }^n}{m^n}+...)$. The omitted terms indicated by ellipsis do not affect inflation for $m\lesssim 1$, but the most popular models with $n=2$ and $4$ for $m\lesssim 1$ are ruled out observationally. Meanwhile in the large $m$ limit the results of the calculations of the tensor to scalar ratio $r$ in the models with $V=V_0(1-\frac{{\varphi }^n}{m^n})$, for all $n$, converge to $r=4/N\lesssim 0.07$, as in chaotic inflation with $V\sim \varphi$, suggesting a reasonably good fit to the Planck data. We show, however, that this is an artifact related to the inconsistency of the model $V=V_0(1-\frac{{\varphi }^n}{m^n})$ at $\varphi >m$. Consistent generalizations of this model in the large $m$ limit typically lead to a much greater value $r=8/N$, which negatively affects the observational status of hilltop inflation. Similar results are valid for D-brane inflation with $V=V_0(1-\frac{m^n}{{\varphi }^n})$, but consistent generalizations of D-brane inflation models may successfully complement $\alpha$-attractors in describing most of the area in the ($n_s$, $r$) space favored by Planck 2018.

Comments: 17 pages, 9 figures, very minor changes, a reference added