Curvaton-assisted hilltop inflation

TL;DR

This work tackles the challenges of hilltop inflation by introducing a curvaton field σ that couples to the inflaton φ, solving the initial-value problem and enabling sub-Planckian hilltop realizations for p=3 and p=4. A stochastic Langevin-diffusion framework reveals an attractor-like universal onset σ_* that makes the onset of hilltop inflation largely independent of initial conditions, with the curvaton subsequently shaping curvature perturbations and decoupling the main observables from the rigid single-field predictions. A Bayesian analysis against Planck and ACT data shows viable parameter spaces with Λ around the GUT scale and μ in the sub-Planckian range, predicting a small but detectable tensor-to-scalar ratio on the order of r ~ 10^{-3} and a modest negative f_NL ~ O(0.1). These results broaden the landscape of testable inflationary models and provide concrete, falsifiable predictions for next-generation CMB experiments such as LiteBIRD and CMB-S4.

Abstract

Following the recent Atacama Cosmology Telescope (ACT) results, we consider hilltop inflation where the inflaton is coupled to a curvaton, simultaneously addressing two main challenges faced by conventional hilltop inflation models: the initial-value problem; and their viability for sub-Planckian field values. In standard single-field hilltop inflation, the inflaton must start extremely close to the maximum of the potential, raising concerns about the naturalness of the initial conditions. We demonstrate that the curvaton field not only solves the initial-value problem, but also opens up parameter space through modifying the curvature perturbation power spectrum, reviving the cubic and quartic hilltop inflation models in the sub-Planckian regime. We find viable parameter space consistent with the recent cosmological observations, and predict a sizable tensor-to-scalar ratio that can be tested in the next-generation Cosmic Microwave Background (CMB) experiments.

Figures (5)

• Figure 1: Comparison between the stochastic paths of fields using the Markov-chain Monte Carlo (MCMC) simulation and the root-mean-square (RMS) approximation in the cubic hilltop model, where we set $\Lambda = 2.7\times10^{-3}\,M_{\rm Pl}$, $\mu = 0.5\,M_{\rm Pl}$, $\lambda = 1.6 \times 10^{-3}$, $m_\phi = 2\times 10^{-7}M_{\rm Pl}$ and $m_\sigma = 10^{-11}M_{\rm Pl}$. The gray lines depict the field trajectories initialized at the yellow point ($\phi_0=0, \sigma_0=2\sigma_{\rm c}$), and terminated once they cross into the classical region $[M^2_{\rm Pl}|V_\phi/V| > H/(2\pi)]$, indicated by the orange shading. The solid red line denotes the statistical average of the fastest 50% of all successfully escaped trajectories. The dashed blue curve represents the RMS-approximated path, obtained by solving the Langevin equations in terms of mean-square values of the fields.
• Figure 2: The RMS-approximated paths for different starting points in the cubic hilltop model. Model parameters in the scalar potential take the same values as those in Fig. \ref{['fig:trajectories']}.
• Figure 3: Upper panel: The 1D marginalized and 2D joint posterior probability distributions for the model parameters $\{\mu, \Lambda, \lambda\}$ in the cubic hilltop model, where we fix $R = 2000$, $m_\phi = 2\times10^{-7} M_{\rm Pl}$, and $m_\sigma = 10^{-11} M_{\rm Pl}$. Constraints are derived from an MCMC Bayesian analysis incorporating observational data for $n_s$ and $A_s$ from Planck18 (TT,TE,EE+lowE) (blue) and P-ACT-LB (red), as well as the upper limit on the tensor-to-scalar ratio $r < 0.036$ at 95% C.L. from BICEP/Keck18 (BK18). The inner and outer contours in the 2D plots correspond to the 68% and 95% credible intervals, respectively. Lower Panel: The predicted values of $r$ as a function of $\mu/M_{\rm Pl}$. Solid lines show the median values from the posterior distributions using Planck18 (blue) and P-ACT-LB (red) data, with shaded bands indicating the $68\%$ credible intervals.
• Figure 4: Upper panel: The 1D marginalized and 2D joint posterior probability distributions for the model parameters $\{\mu, \Lambda, \lambda\}$ in the quartic hilltop model, where we fix $R = 500$, $m_\phi = 2\times10^{-7} M_{\rm Pl}$, and $m_\sigma = 10^{-11} M_{\rm Pl}$. We use the same experimental constraints as in Fig. \ref{['fig:cubic_results']}. Lower Panel: The predicted values of $r$ as a function of $\mu/M_{\rm Pl}$. Solid lines show the median values from the posterior distributions using Planck18 (blue) and P-ACT-LB (red) data, with shaded bands indicating the $68\%$ credible intervals.
• Figure 5: Relations between the tensor-to-scalar ratio $r$ and the spectral index $n_s$ in the cubic and quartic hilltop models. The pink- and orange-shaded contours are the constraints from the P-ACT-LB-BK18 and Planck-LB-BK18 results, with the darker and lighter colors denoting the 68% and 95% C.L. allowed regions, respectively AtacamaCosmologyTelescope:2025nti. Blue lines correspond to the predicted $r-n_s$ relations in the single-field hilltop models (trans-Planckian regime with $\mu \gg M_{\rm Pl}$). The green lines represent the $r-n_s$ relations in the curvaton-assisted hilltop models, where $\mu \lesssim M_{\rm Pl}$, $\lambda$ is fixed at $1.6 \times 10^{-3}$ for the cubic hilltop and $6 \times 10^{-4}$ for the quartic hilltop, respectively, and $\mathcal{A}_s$ is taken to be close to its best-fit value inferred from the observations.