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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.00375 |
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| _version_ | 1866911841323581440 |
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| author | Hong, Deog Ki Jiang, Jie Yeom, Dong-han |
| author_facet | Hong, Deog Ki Jiang, Jie Yeom, Dong-han |
| contents | In this study, we generalize the Fokker-Planck equation to two-dimensional cases, including potential functions with periodic boundary conditions and piecewise-defined structures, to analyze the probability distribution in multi-field inflationary models. We employ the spectral method for spatial derivatives and the Crank-Nicolson method for the time evolution to solve the equation numerically for the slow-roll inflation. We find that the distribution in the Fokker-Planck equation was determined by the two-dimensional potential combined slow-roll parameters. And the volume weighting effect makes the distribution in the Fokker-Planck Volume equation is determined by the potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_00375 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Numerical Investigation of Two-Dimensional Fokker-Planck Equation in Inflationary Models: Importance of Slow-Roll Parameters Hong, Deog Ki Jiang, Jie Yeom, Dong-han General Relativity and Quantum Cosmology In this study, we generalize the Fokker-Planck equation to two-dimensional cases, including potential functions with periodic boundary conditions and piecewise-defined structures, to analyze the probability distribution in multi-field inflationary models. We employ the spectral method for spatial derivatives and the Crank-Nicolson method for the time evolution to solve the equation numerically for the slow-roll inflation. We find that the distribution in the Fokker-Planck equation was determined by the two-dimensional potential combined slow-roll parameters. And the volume weighting effect makes the distribution in the Fokker-Planck Volume equation is determined by the potential. |
| title | Numerical Investigation of Two-Dimensional Fokker-Planck Equation in Inflationary Models: Importance of Slow-Roll Parameters |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2310.00375 |