Cosmic structure from the path integral of classical mechanics and its comparison to standard perturbation theory
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| Format: | Preprint |
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2025
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| _version_ | 1866908824094375936 |
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| author | Sipp, Marvin Heisler, Hannes Bartelmann, Matthias |
| author_facet | Sipp, Marvin Heisler, Hannes Bartelmann, Matthias |
| contents | We investigate cosmic structure formation in the framework of a path-integral formulation of an $N$-particle ensemble in phase space, dubbed Resummed Kinetic Field Theory (RKFT), up to one-loop perturbative order. In particular, we compute power spectra of the density contrast, the divergence and curl of the momentum density and arbitrary $n$-point cumulants of the stress tensor. In contrast to earlier works, we propose a different method of sampling initial conditions, with a Gaussian initial phase-space density. Doing so, we exactly reproduce the corresponding results from Eulerian standard perturbation theory (SPT) at one-loop order, showing that formerly found deviations can be fully attributed to inconsistencies in the previous sampling method. Since, in contrast to SPT, the full phase-space description does not assume a truncation of the Vlasov hierarchy, our findings suggest that nonperturbative techniques are required to accurately capture the physics of cosmic structure formation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_02692 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cosmic structure from the path integral of classical mechanics and its comparison to standard perturbation theory Sipp, Marvin Heisler, Hannes Bartelmann, Matthias Cosmology and Nongalactic Astrophysics Statistical Mechanics We investigate cosmic structure formation in the framework of a path-integral formulation of an $N$-particle ensemble in phase space, dubbed Resummed Kinetic Field Theory (RKFT), up to one-loop perturbative order. In particular, we compute power spectra of the density contrast, the divergence and curl of the momentum density and arbitrary $n$-point cumulants of the stress tensor. In contrast to earlier works, we propose a different method of sampling initial conditions, with a Gaussian initial phase-space density. Doing so, we exactly reproduce the corresponding results from Eulerian standard perturbation theory (SPT) at one-loop order, showing that formerly found deviations can be fully attributed to inconsistencies in the previous sampling method. Since, in contrast to SPT, the full phase-space description does not assume a truncation of the Vlasov hierarchy, our findings suggest that nonperturbative techniques are required to accurately capture the physics of cosmic structure formation. |
| title | Cosmic structure from the path integral of classical mechanics and its comparison to standard perturbation theory |
| topic | Cosmology and Nongalactic Astrophysics Statistical Mechanics |
| url | https://arxiv.org/abs/2507.02692 |