Gravitational turbulence: the small-scale limit of the cold-dark-matter power spectrum
The matter power spectrum, ๐โก(๐), 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 ๐ spatial dimensions, ๐โก(๐) has a universal ๐โ๐ asymptotic scaling with the wave number ๐,...
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| Main Authors: | , , , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
3 September, 2025
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| In: |
Physical review
Year: 2025, Volume: 112, Issue: 6, Pages: 1-23 |
| ISSN: | 2470-0029 |
| DOI: | 10.1103/ychs-2d5p |
| Online Access: | 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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| Author Notes: | Yonadav Barry Ginat, Michael L. Nastac, Robert J. Ewart, Sara Konrad, Matthias Bartelmann, and Alexander A. Schekochihin |
| Summary: | The matter power spectrum, ๐โก(๐), 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 ๐ spatial dimensions, ๐โก(๐) has a universal ๐โ๐ asymptotic scaling with the wave number ๐, for ๐ โซ๐nl, where ๐โ1nl 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 systemโs 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 ๐ dependence of the power spectrum. A parallel is drawn to Batchelor turbulence in hydrodynamics, where large scales mix smaller ones via tidal interactions. The ๐โ๐ scaling is also derived by expressing ๐โก(๐) 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 functionโits nonvanishing only on a ๐-dimensional submanifold of phase spaceโunderpins both approaches. The theory is accompanied by 1D Vlasov-Poisson simulations, which confirm it. |
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| Item Description: | Gesehen am 27.01.2026 |
| Physical Description: | Online Resource |
| ISSN: | 2470-0029 |
| DOI: | 10.1103/ychs-2d5p |