Nonlinear Lattice Framework for Inflation: Bridging stochastic inflation and the $δ{N}$ formalism
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arXiv
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| Natura: | Preprint |
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2026
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| author | Saha, Pankaj Tada, Yuichiro Urakawa, Yuko |
| author_facet | Saha, Pankaj Tada, Yuichiro Urakawa, Yuko |
| contents | Understanding when inflationary perturbations become genuinely nonlinear near the horizon crossing requires methods that go beyond both linear perturbation theory and the gradient expansion. In this work, we introduce a nonlinear lattice framework for single-field inflation based on a shear-free, locally Friedmann-Lemaître-Robertson-Walker geometry. This approach captures inhomogeneous local expansion rates, curvature contributions to the local Friedmann equation, and proper-volume weighting at a fraction of the computational cost of full numerical relativity. We construct fully nonlinear $δN$ observables on uniform-density slices, together with other practical time-dependent estimators for the curvature perturbations. After validating the framework in a standard slow-roll regime, we apply it to Starobinsky's linear-potential model featuring an intermittent ultra-slow-roll (USR) phase and a sharp potential transition. During this non-attractor USR regime, the lattice captures the separation of curvature perturbation estimators, the growth and subsequent stabilisation of non-Gaussianity, and a transient weakening of the shear-free approximation when the inflaton velocity becomes very small. Our framework provides a practical intermediate approach between rigid background lattice simulations and full numerical relativity, offering a nonlinear bridge between lattice methods, the $δN$ formalism, and the stochastic inflation formalism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00978 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonlinear Lattice Framework for Inflation: Bridging stochastic inflation and the $δ{N}$ formalism Saha, Pankaj Tada, Yuichiro Urakawa, Yuko General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Understanding when inflationary perturbations become genuinely nonlinear near the horizon crossing requires methods that go beyond both linear perturbation theory and the gradient expansion. In this work, we introduce a nonlinear lattice framework for single-field inflation based on a shear-free, locally Friedmann-Lemaître-Robertson-Walker geometry. This approach captures inhomogeneous local expansion rates, curvature contributions to the local Friedmann equation, and proper-volume weighting at a fraction of the computational cost of full numerical relativity. We construct fully nonlinear $δN$ observables on uniform-density slices, together with other practical time-dependent estimators for the curvature perturbations. After validating the framework in a standard slow-roll regime, we apply it to Starobinsky's linear-potential model featuring an intermittent ultra-slow-roll (USR) phase and a sharp potential transition. During this non-attractor USR regime, the lattice captures the separation of curvature perturbation estimators, the growth and subsequent stabilisation of non-Gaussianity, and a transient weakening of the shear-free approximation when the inflaton velocity becomes very small. Our framework provides a practical intermediate approach between rigid background lattice simulations and full numerical relativity, offering a nonlinear bridge between lattice methods, the $δN$ formalism, and the stochastic inflation formalism. |
| title | Nonlinear Lattice Framework for Inflation: Bridging stochastic inflation and the $δ{N}$ formalism |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2604.00978 |