Gravitational turbulence: the small-scale limit of the cold-dark-matter power spectrum
The matter power spectrum, 𝑃(𝑘), is one of the fundamental quantities in the study of large-scale structure in cosmology. Here, we study its small-scale asymptotic limit, and show that for cold dark matter in 𝑑 spatial dimensions, 𝑃(𝑘) has a universal 𝑘−𝑑 asymptotic scaling with the wave number 𝑘,...
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| Hauptverfasser: | , , , , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
3 September, 2025
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| In: |
Physical review
Year: 2025, Jahrgang: 112, Heft: 6, Pages: 1-23 |
| ISSN: | 2470-0029 |
| DOI: | 10.1103/ychs-2d5p |
| Online-Zugang: | Verlag, kostenfrei, Volltext: https://doi.org/10.1103/ychs-2d5p Verlag, kostenfrei, Volltext: https://link.aps.org/doi/10.1103/ychs-2d5p 
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| Verfasserangaben: | Yonadav Barry Ginat, Michael L. Nastac, Robert J. Ewart, Sara Konrad, Matthias Bartelmann, and Alexander A. Schekochihin |
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| 520 | |a The matter power spectrum, (), is one of the fundamental quantities in the study of large-scale structure in cosmology. Here, we study its small-scale asymptotic limit, and show that for cold dark matter in spatial dimensions, () has a universal − asymptotic scaling with the wave number , for ≫nl, where −1nl denotes the length scale at which nonlinearities in gravitational interactions become important. We propose a theoretical explanation for this scaling, based on a nonperturbative analysis of the system’s phase-space structure. Gravitational collapse is shown to drive a turbulent phase-space flow of the quadratic Casimir invariant, where the linear and nonlinear time scales are balanced, and this balance dictates the dependence of the power spectrum. A parallel is drawn to Batchelor turbulence in hydrodynamics, where large scales mix smaller ones via tidal interactions. The − scaling is also derived by expressing () as a phase-space integral in the framework of kinetic field theory, which is analyzed by the saddle-point method; the dominant critical points of this integral are precisely those where the time scales are balanced. The coldness of the dark-matter distribution function—its nonvanishing only on a -dimensional submanifold of phase space—underpins both approaches. The theory is accompanied by 1D Vlasov-Poisson simulations, which confirm it. | ||
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