Highly suppressed tensor-to-scalar ratio from a modified Lennard-Jones inflationary potential

TL;DR

This work addresses whether extremely small tensor amplitudes can be achieved in a minimal single-field inflation model driven by potential dynamics alone. It introduces a modified Lennard-Jones potential with a smooth minimum and a large-field plateau, and shows through slow-roll analysis that $n_s$ can match observations while $r$ is suppressed to as low as $10^{-7}$. The approach requires no non-minimal couplings or noncanonical kinetic terms, and reheating proceeds via gravitationally suppressed decays with $T_{reh} \sim 3\times10^{10}$ GeV. Overall, it provides a simple, self-contained plateau-like inflation benchmark with potential implications for upcoming CMB probes such as LiteBIRD and CMB-S4.

Abstract

The increasingly stringent observational bounds on primordial gravitational waves strongly constrain inflationary model building, favoring scenarios that predict highly suppressed tensor perturbations. While many viable constructions rely on non-canonical kinetic terms, non-minimal couplings, or modifications of gravity, it remains an open question whether comparably small tensor amplitudes can emerge within a minimal, single-field framework driven solely by potential dynamics. In this work we propose a novel inflationary scenario based on a modified Lennard-Jones potential. Inspired by a well-known interaction potential in molecular physics, the proposed form naturally combines a smooth minimum with an extended flat plateau at large field values. This intrinsic structure supports slow-roll inflation and ensures a graceful exit without introducing additional degrees of freedom. We perform a detailed analysis of the inflationary dynamics and confront the model with current observational constraints. We find that the scalar spectral index is fully consistent with CMB data, while the tensor-to-scalar ratio is predicted to be extremely small, reaching values as low as $r\sim10^{-7}$. Finally, the running of the scalar spectral index is also found to be small, well withing the 1$σ$ recent observational bounds from Atacama Cosmology Telescope.

Figures (4)

• Figure 1: The modified Lennard-Jones potential $V(\phi)$ of Eq. (\ref{['LJpotential']}) for $V_0 \simeq 10^{65}\,{\rm GeV}^4$, and for $\beta= 10^{19}\,{\rm GeV}$ (black-solid curve) and $\beta=5\times 10^{18}\,{\rm GeV}$ (red-dashed curve).
• Figure 2: The predictions of the inflationary scenario based on the modified Lennard-Jones potential (\ref{['LJpotential']}) on the $n_{\mathrm{s}}-r$ plane. The left curve corresponds to e-folding number $N=50$, with $\beta$ varying from $10^{16}$ GeV to $3\times 10^{19}$ GeV, while the middle and right curves correspond to $N=55$ and $N=60$, respectively, with the same variance of $\beta$. In all curves $V_0$ is set around $V_0= 10^{65}$GeV$^4$ in order to obtain $A_s = 2 \times 10^{-9}$.
• Figure 3: The predictions of Fig. \ref{['rns']} on top of the 1$\sigma$ and 2$\sigma$ Planck 2018 TT,TE,EE+lowE+lensing +BK15+BAO results Planck:2018jri.
• Figure 4: The predictions of the inflationary scenario based on the modified Lennard-Jones potential (\ref{['LJpotential']}) on the running spectral index $\alpha_s$. The left curve corresponds to e-folding number $N=50$, with $\beta$ varying from $10^{16}$ GeV to $3\times 10^{19}$ GeV, while the middle and right curves corresponds to $N=55$ and $N=60$, respectively, with the same variance of $\beta$. In all curves $V_0$ is set around $V_0= 10^{65}$GeV$^4$ in order to obtain $A_s = 2 \times 10^{-9}$. Additionally, we present the 1$\sigma$ (yellow) and 2$\sigma$ (light yellow) contours for the Atacama Cosmology Telescope (P-ACT) results ACT:2025tim.