Memoirs of the curvaton: non-perturbative non-Gaussianity and supermassive primordial black holes

S. Allegrini, A. J. Iovino, G. Perna, H. Veermäe

First listed 2026-06-29 | Last updated 2026-06-26

Abstract

The curvaton provides a simple mechanism for generating strongly non-Gaussian curvature perturbations after inflation, with potentially important consequences on small scales. We study curvaton dynamics beyond the standard quadratic potential and construct the local non-Gaussian map $ζ=F(ζ_{\rm G})$ relating the curvature perturbation to an auxiliary Gaussian field $ζ_{\rm G}$. Curvaton self-interactions make the onset of oscillations field dependent and modify the effective equation of state once the curvaton enters the adiabatic regime. We incorporate these effects using the abbreviated action, which provides a compact way to connect the frozen and oscillatory regimes and exposes sources of non-Gaussianity absent in the purely quadratic case. We apply the formalism to quadratic, monomial, quartic, and cosine potentials, for which we derive the mapping $F(ζ_{\rm G})$ and show that self-interactions can either enhance or suppress the resulting non-Gaussianity depending on the potential and initial conditions. We consider non-perturbative aspects in the strongly non-Gaussian regime, and show how strong non-Gaussianity can suppress the power spectrum. As an application, we provide a bottom-up scenario in which strongly positive curvaton non-Gaussianity allows primordial supermassive black hole seeds at peak amplitudes $\mathcal{A}_{\rm pk}\sim10^{-5}$, which are compatible with the COBE/FIRAS $μ$-distortion bounds. This opens a new primordial scenario for the Little Red Dots observed by the JWST. The axion-like curvaton provides a particularly natural setting for this mechanism.

Short digest

This paper derives the full local non-Gaussian map ζ = F(ζ_G) for curvaton models beyond the standard quadratic case, using an abbreviated-action treatment that tracks field-dependent oscillation onset and changes to the effective equation of state in the adiabatic regime. Across quadratic, monomial, quartic, and cosine potentials, the authors show that self-interactions can either enhance or suppress the resulting non-Gaussianity, and that in the strongly non-Gaussian regime the full non-perturbative mapping can substantially suppress the curvature power spectrum relative to naive perturbative expectations. The main application is a bottom-up primordial route to supermassive black-hole seeds: strongly positive curvaton non-Gaussianity can produce PBH seeds with peak amplitudes A_pk ~ 10^-5 while remaining compatible with COBE/FIRAS μ-distortion bounds. That makes axion-like cosine curvatons an especially natural version of a primordial seeding channel for JWST Little Red Dots.

Key figures to inspect

• Figure 5. This is the key self-interaction figure for the quartic case: it compares numerical and analytical determinations of F(ζ_G) and then scans how the mapping changes as the self-interaction strength s moves from the quadratic toward the quartic limit. Use it to show concretely that self-interactions do not just perturb the quadratic result, but can qualitatively reshape the non-Gaussian map that drives the paper’s later phenomenology.
• Figure 6. This is the most important potential-specific figure for the paper’s preferred axion-like scenario. The left panel shows how the cosine potential changes N_dec(σ)-N_0, while the right panel displays the resulting F(ζ_G) for several benchmark choices of f and background field, making clear why the cosine curvaton can naturally generate the strong positive non-Gaussianity highlighted in the abstract.
• Figure 9. This figure connects the derived non-Gaussian map directly to the curvature power spectrum. The left panel shows how F(ζ_G) changes with r_dec, and the right panel demonstrates the resulting full non-Gaussian power spectra, which is central to the paper’s claim that strong non-Gaussianity can suppress power in a way missed by truncated treatments.
• Figure 11. This is the conclusion-driving phenomenology figure. It combines the full non-Gaussian power spectra with μ-distortion constraints and PBH abundance, and directly shows the parameter dependence behind the headline result that supermassive-PBH seeds can be produced at peak amplitudes compatible with COBE/FIRAS bounds.