Rigorous explanation of the near‑universal infrared shape in large‑NG curvature spectra

Determine a rigorous explanation for the observed nearly universal infrared behavior of the curvature perturbation power spectrum in large‑non‑Gaussianity ultra‑slow‑roll/constant‑roll/successive slow‑roll inflationary scenarios as revealed by the lattice simulations.

Background

In large‑non‑Gaussianity models featuring an ultra‑slow‑roll stage followed by constant‑roll and slow‑roll phases, the lattice simulations reveal that the infrared portion of the curvature power spectrum tends toward a nearly universal shape across parameter choices with sufficiently large peak amplitudes.

The authors suggest an intuitive connection to backreaction—namely that long‑wavelength modes may probe similar regions of the potential at similar times—but explicitly acknowledge that a definitive, rigorous explanation is currently lacking.

References

Interestingly, for all models with $\mathcal{P}{\rm max}_{\zeta,\rm tree}\geq 10{-2}$, the IR part of the spectrum appears to approach a nearly universal shape. While we do not currently have a rigorous explanation for this behaviour, it may be intuitively related to the fact that, due to backreaction, these IR modes probe essentially the same region of the potential at similar times during inflation.

— Lattice simulations of scalar-induced gravitational waves from inflation  (2604.03628 - Caravano et al., 4 Apr 2026) in Section 5.2, Simulation results — Large non‑Gaussianity