Exploring Ultra-Slow-Roll Inflation in Composite Pseudo-Nambu-Goldstone Boson Models: Implications for Primordial Black Holes and Gravitational Waves

TL;DR

The paper investigates ultra-slow-roll inflation in a single-field model where the inflaton is a pseudo-Nambu-Goldstone boson from a composite sector, with a periodic non-minimal coupling to gravity that flattens the potential at large field values. By combining analytical inflection-point criteria with full Mukhanov-Sasaki computations, it identifies parameter regions that realize USR and amplify curvature perturbations, yielding primordial black holes in the ultra-light mass range $M_{\mathrm{PBH}} \in [10^3,10^5]\,\mathrm{g}$ and a second-order gravitational-wave background peaked at high frequencies. The PBH production relies on a significant enhancement of the power spectrum and is analyzed via Press-Schechter formalism, with the resulting GW signals residing in a frequency gap between planned interferometers and resonant-cavity detectors. Current CMB constraints on the spectral index $n_s$, particularly from ACT, place strong tension on the viable parameter space, motivating potential extensions such as explicit symmetry breaking or UV completions; memory-burden evaporation offers a speculative mechanism to stabilize ultra-light PBHs as dark matter and shapes the observational prospects. Overall, the work presents a novel, predictive framework linking composite-sector inflation to ultra-light PBHs and high-frequency gravitational waves, along with clear directions for theoretical refinements and experimental tests.

Abstract

We study inflation driven by a scalar potential arising from composite-sector dynamics, inspired by generalized composite Higgs models. The introduction of a non-minimal coupling, possessing the same functional form as the potential, induces a flattening at large field values that enables successful inflation. We analyze the conditions for ultra-slow-roll inflation, which leads to enhanced curvature perturbations, by combining analytical criteria near the inflection point with comprehensive numerical scans of the parameter space. The region consistent with Cosmic Microwave Background constraints and yielding approximately $N_e \approx 55\text{-}60$ e-folds also predicts primordial black holes with masses in the range $10^3\text{-}10^5\,\mathrm{g}$. Although such ultra-light primordial black holes are typically expected to have evaporated, recent proposals invoking evaporation suppression via memory-burden effects could allow their survival as viable dark matter candidates. Under this assumption, the induced gravitational wave signal peaks in a frequency gap between standard interferometers and resonant-cavity experiments, motivating exploration of this observational frontier.

Figures (7)

• Figure 1: Schematic representation of the numerical algorithm used for benchmark extraction consistent with USR inflationary phase.
• Figure 2: Illustrations corresponding to Benchmark 1 of Table \ref{['benchmark_table']}. Left: Potential in the Jordan frame. Right: Potential in the Einstein frame. The green dots on the curve indicate the inflaton USR trajectory and the dashed-orange line the infaton velocity.
• Figure 3: Predictions for the scalar spectral index $n_s$ as a function of canonically normalized inflaton field, corresponding to Benchmark 1 of Table \ref{['benchmark_table']} with ($\alpha \neq 0$) and without non-minimal coupling ($\alpha = 0$) as shown on the plot legends. The black horizontal dotted-dashed line represents the central value from Planck:2018jri.
• Figure 4: Primordial curvature power spectrum as a function of the wave number, shown both in the slow-roll approximation (blue curve) and as obtained from the full solution of the Mukhanov-Sasaki equation (orange dashed line). The potential parameters correspond to Benchmark 1 listed in Table \ref{['benchmark_table']}. The location of the peak is indicated by a vertical dotted black line and annotated within the figure.
• Figure 5: Spectral index plotted against the predicted number of e-folds from the time the CMB scale exits the horizon until the end of inflation for Benchmark 1 (stars) and Benchmark 5 (squares). The blue and orange shaded regions represent the 3$\sigma$ confidence intervals from Planck Planck:2018jri and ACT ACT:2025fju, respectively. The secondary y-axis shows the approximate PBH masses at the peak of the power spectrum, calculated using the slow-roll approximation for Benchmark 1; we have verified that Benchmark 5 yields similar PBH mass estimates within the same order of magnitude.