BullFrog: Multi-step perturbation theory as a time integrator for cosmological simulations
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| Format: | Preprint |
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2024
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| author | Rampf, Cornelius List, Florian Hahn, Oliver |
| author_facet | Rampf, Cornelius List, Florian Hahn, Oliver |
| contents | Modelling the cosmic large-scale structure can be done through numerical N-body simulations or by using perturbation theory. Here, we present an N-body approach that effectively implements a multi-step forward model based on Lagrangian Perturbation Theory (LPT) in a $Λ$CDM Universe. This is achieved by introducing the second-order accurate BullFrog integrator, which automatically performs 2LPT time steps to second order without requiring the explicit computation of 2LPT displacements. Importantly, we show that BullFrog trajectories rapidly converge to the exact solution as the number of time steps increases, at any moment in time, even though 2LPT becomes invalid after shell-crossing. As a validation test, we compare BullFrog against other N-body integrators and high-order LPT, both for a realistic $Λ$CDM cosmology and for simulations with a sharp UV cutoff in the initial conditions. The latter scenario enables controlled experiments against LPT and, in practice, is particularly relevant for modelling coarse-grained fluids arising in the context of effective field theory. We demonstrate that BullFrog significantly improves upon other LPT-inspired integrators, such as FastPM and COLA, without incurring any computational overhead compared to standard N-body integrators. Implementing BullFrog in any existing N-body code is straightforward, particularly if FastPM is already integrated. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_19049 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | BullFrog: Multi-step perturbation theory as a time integrator for cosmological simulations Rampf, Cornelius List, Florian Hahn, Oliver Cosmology and Nongalactic Astrophysics Computational Physics 85-08 (Primary), 85A40 (Secondary) Modelling the cosmic large-scale structure can be done through numerical N-body simulations or by using perturbation theory. Here, we present an N-body approach that effectively implements a multi-step forward model based on Lagrangian Perturbation Theory (LPT) in a $Λ$CDM Universe. This is achieved by introducing the second-order accurate BullFrog integrator, which automatically performs 2LPT time steps to second order without requiring the explicit computation of 2LPT displacements. Importantly, we show that BullFrog trajectories rapidly converge to the exact solution as the number of time steps increases, at any moment in time, even though 2LPT becomes invalid after shell-crossing. As a validation test, we compare BullFrog against other N-body integrators and high-order LPT, both for a realistic $Λ$CDM cosmology and for simulations with a sharp UV cutoff in the initial conditions. The latter scenario enables controlled experiments against LPT and, in practice, is particularly relevant for modelling coarse-grained fluids arising in the context of effective field theory. We demonstrate that BullFrog significantly improves upon other LPT-inspired integrators, such as FastPM and COLA, without incurring any computational overhead compared to standard N-body integrators. Implementing BullFrog in any existing N-body code is straightforward, particularly if FastPM is already integrated. |
| title | BullFrog: Multi-step perturbation theory as a time integrator for cosmological simulations |
| topic | Cosmology and Nongalactic Astrophysics Computational Physics 85-08 (Primary), 85A40 (Secondary) |
| url | https://arxiv.org/abs/2409.19049 |