Stochastic Inflation in Numerical Relativity
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arXiv
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| Format: | Preprint |
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2025
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| author | Launay, Yoann L. Rigopoulos, Gerasimos I. Shellard, E. Paul S. |
| author_facet | Launay, Yoann L. Rigopoulos, Gerasimos I. Shellard, E. Paul S. |
| contents | A set of 3+1 equations for stochastic inflation incorporating all metric and scalar matter degrees of freedom, first presented in previous work, are re-derived in a gauge invariant manner. We then present numerical implementations of these stochastic equations, cast in the BSSN formulation of Numerical Relativity, demonstrating their efficacy in both a slow-roll and an ultra slow-roll scenario. We find the evolution is correctly reproduced for all the dynamical variables, and the energy and momentum constraints are well-satisfied. This demonstrates that the stochastic equations are theoretically and numerically robust and ready to be applied to a wider inflationary landscape. Our simulations result in real space realizations of the fully non-linear stochastic dynamics with \new{gradients and anisotropic expansion retained. This work generalizes standard stochastic inflation, inflationary numerical relativity and lattice cosmology, opening up the possibility for reliable predictions of non-perturbative phenomena and providing} precise initial conditions for subsequent cosmological eras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14649 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic Inflation in Numerical Relativity Launay, Yoann L. Rigopoulos, Gerasimos I. Shellard, E. Paul S. General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory A set of 3+1 equations for stochastic inflation incorporating all metric and scalar matter degrees of freedom, first presented in previous work, are re-derived in a gauge invariant manner. We then present numerical implementations of these stochastic equations, cast in the BSSN formulation of Numerical Relativity, demonstrating their efficacy in both a slow-roll and an ultra slow-roll scenario. We find the evolution is correctly reproduced for all the dynamical variables, and the energy and momentum constraints are well-satisfied. This demonstrates that the stochastic equations are theoretically and numerically robust and ready to be applied to a wider inflationary landscape. Our simulations result in real space realizations of the fully non-linear stochastic dynamics with \new{gradients and anisotropic expansion retained. This work generalizes standard stochastic inflation, inflationary numerical relativity and lattice cosmology, opening up the possibility for reliable predictions of non-perturbative phenomena and providing} precise initial conditions for subsequent cosmological eras. |
| title | Stochastic Inflation in Numerical Relativity |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.14649 |