On hilltop and brane inflation after Planck

Renata Kallosh; Andrei Linde

doi:10.1088/1475-7516/2019/09/030

paper

On hilltop and brane inflation after Planck

arXiv:1906.02156 · doi:10.1088/1475-7516/2019/09/030

Abstract

Hilltop inflation models are often described by potentials $V = V_{0} (1 - \frac{ϕ ^{n}}{m ^{n}} + ...)$ . The omitted terms indicated by ellipsis do not affect inflation for $m ≲ 1$ , but the most popular models with $n = 2$ and $4$ for $m ≲ 1$ 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 $V = V_{0} (1 - \frac{ϕ ^{n}}{m ^{n}})$ , for all $n$ , converge to $r = 4/ N ≲ 0.07$ , as in chaotic inflation with $V \sim ϕ$ , suggesting a reasonably good fit to the Planck data. We show, however, that this is an artifact related to the inconsistency of the model $V = V_{0} (1 - \frac{ϕ ^{n}}{m ^{n}})$ at $ϕ > m$ . 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 $V = V_{0} (1 - \frac{m ^{n}}{ϕ ^{n}})$ , but consistent generalizations of D-brane inflation models may successfully complement $α$ -attractors in describing most of the area in the ( $n_{s}$ , $r$ ) space favored by Planck 2018.

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

On hilltop and brane inflation after Planck

Abstract

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