# On hilltop and brane inflation after Planck

## TL;DR

This paper critically examines hilltop and brane inflation models in light of Planck data, revealing that certain popular models are inconsistent or less favored, and proposes more consistent generalizations that better fit observational constraints.

## Contribution

The paper identifies inconsistencies in common hilltop and brane inflation models and introduces more consistent large-mass generalizations that align better with Planck observations.

## Key findings

- Models with $n=2$ and $4$ are observationally ruled out.
- Inconsistent models suggest $r=4/N$, but consistent versions imply $r=8/N$, affecting fit to data.
- D-brane inflation models can complement $eta$-attractors in explaining Planck data.

## Abstract

Hilltop inflation models are often described by potentials $V = V_{0}(1-{\phi^{n}\over m^{n}}+...)$. 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 $V = V_{0}(1-{\phi^{n}\over m^{n}})$, for all $n$, converge to $r= 4/N \lesssim 0.07$, as in chaotic inflation with $V \sim \phi$, suggesting a reasonably good fit to the Planck data. We show, however, that this is an artifact related to the inconsistency of the model $V = V_{0}(1-{\phi^{n}\over m^{n}})$ at $\phi > m$. 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 $V = V_{0}(1-{m^{n}\over \phi^{n}})$, 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.