Hilltop Inflation

TL;DR

This work shows that hilltop inflation, where inflation occurs near a local potential maximum, is a generic and theoretically attractive framework that alleviates the ${\eta}$-problem and reduces sensitivity to initial conditions by naturally accommodating eternal inflation. The authors analyze slow-roll dynamics, derive observational constraints (notably a small tensor fraction $r$ for monotonic slopes), and explore several realizations including modular, natural/chaotic, and running-mass scenarios. They demonstrate how Planck-suppressed terms readily convert standard ${F}$- and ${D}$-term models into hilltop forms, easing fine-tuning and broadening viable parameter space, especially when the curvature perturbation is sourced by orthogonal fields. The paper concludes that hilltop inflation is both generic and observationally consistent, with most models predicting negligible tensor modes unless specific conditions (e.g., Natural Inflation) yield detectable signals, and highlights eternal hilltop inflation as a natural initial-condition mechanism. Overall, hilltop inflation provides a robust, versatile framework linking particle physics potentials to cosmological observations and pre-inflationary conditions.

Abstract

We study `hilltop' inflation, in which inflation takes place near a maximum of the potential. Viewed as a model of inflation after the observable Universe leaves the horizon (observable inflation) hilltop inflation is rather generic. If the potential steepens monotonically, observable hilltop inflation gives a tiny tensor fraction (r< 0.002). The usual F- and D-term models may easily be transmuted to hilltop models by Planck-suppressed terms, making them more natural. The only commonly-considered model of observable inflation which is definitely not hilltop is tree-level hybrid inflation. Viewed instead as an initial condition, we explain that hilltop inflation is more generic than seems to have been previously recognized, adding thereby to the credibility of the idea that eternal inflation provides the pre-inflationary initial condition.

Figures (5)

• Figure 1: The upper bound on the height of hilltop inflation. The dashed (black) curve is obtained using the slow-roll approximation while the continuous (green) curve is obtained using the better fast-roll approximation. The top horizontal line represents the bound from the absence of a tensor signal in the CMB, which is seen to be automatic for hilltop inflation. The bottom horizontal line represents the absolute lower bound coming from BBN. If the inflaton perturbation generates the observed curvature perturbation, the observational bound on the spectral index places $|\eta_0|$ to the left of the vertical dash-dot (dark green) line.
• Figure 2: $n_S - 1$ versus $\eta_0$ for the Natural Inflation scenario. The shaded region corresponds to the present WMAP/SDSS bound data.
• Figure 3: Sketch of the inflationary potential for the $F$/$D$ - term scenario when including the non renormalizable terms (continuous line) and the original potential (dashed line).
• Figure 4: The VEV of the waterfall field as a function of $\eta_m$. Any point in the light yellow area is allowed. The upper horizontal (red) line stands for the bound on tensor fluctuations while the lower one stands for the BBN bound. The vertical dot-dash lines are for the the bound on $n_S$.
• Figure 5: Sketch of the hilltop potential of Eq. (\ref{['hill']}) when ${\cal F}'$ is negative.