Building on the recent lattice simulations of ultraslow-roll dynamics presented in [A. Caravano et al., Phys. Rev. D 111, 063518 (2025).], we investigate the role of the nonlinear relation between the inflaton field configuration and the curvature perturbation $\zeta$, the key observable after inflation. Using a nonperturbative $\delta N$ approach applied to the lattice output, we generate fully nonlinear three-dimensional maps of $\zeta$. This calculation captures both the non-Gaussianity arising from the nonlinear mapping between $\varphi$ and $\zeta$, and the intrinsic non-Gaussianity generated around Hubble crossing by the nonlinear field dynamics, which is neglected in stochastic approaches. We find that the nonlinear mapping has a profound impact on the statistics, significantly enhancing the positive tail of the $\zeta$ probability distribution, with important implications for observable quantities. A central part of this work is the comparison with the standard perturbative treatment based on a gauge transformation, which allows us to quantify when and how the perturbative picture breaks down as fluctuations grow large. Together with the above article, this work sets the basis for robust, nonperturbative predictions of primordial black hole production and scalar-induced gravitational wave emission from inflation using lattice simulations.

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• Cosmology
• Gravitational waves
• Inflation
• Primordial black holes
• Astrophysical & cosmological simulations