More hilltop inflation models

TL;DR

This work develops an analytic framework for hilltop inflation across a broad class of potentials $V(\phi)=V_0 \pm \tfrac{1}{2} m^2 \phi^2 - \lambda \frac{\phi^p}{M_{\rm P}^{p-4}}+\cdots$, using a two-term approximation to derive expressions for the curvature perturbation spectrum ${\cal P}_\zeta$, the spectral index $n$, and its running $n'$. By examining regimes with $\eta_0$ and $p$ of various signs and magnitudes, the authors show that hilltop dynamics can naturally yield $n\approx 0.95$ in several models, including modular, new, F-/D-term, and hilltop versions of hybrid inflation, while $n'$ provides a powerful discriminator. They also demonstrate constraints from black hole formation and show how SUSY or brane-inspired constructions can suppress problematic terms to achieve observationally consistent predictions. Overall, the paper provides analytic tools to map the viable parameter space of hilltop inflation and argues that upcoming measurements of $n'$ could distinguish among competing hilltop scenarios.

Abstract

Using analytic expressions, we explore the parameter space for hilltop inflation models with a potential of the form $V_0\pm m^2φ^2 -aφ^p$. 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 $|n-1|\lsim 1$.

Figures (25)

• Figure 1: Model1. Two-term approximation about the hilltop.
• Figure 2: Model2. Hilltop mutated/brane hybrid inflation.
• Figure 3: Model3. Hilltop original hybrid inflation.
• Figure 4: $p\geqslant3$, contours of $n$ in the $\log(-\eta_0)$-$p$ plane.
• Figure 5: $p<0$, contours of $n$ in the $\log(-\eta_0)$-$p$ plane.