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  • Open Access

Vlasov perturbation theory applied to ΛCDM

Mathias Garny1,*, Dominik Laxhuber1,†, and Román Scoccimarro2,‡

  • 1Physik Department T31, Technische Universität München, James-Franck-Straße 1, D-85748 Garching, Germany
  • 2Center for Cosmology and Particle Physics, Department of Physics, New York University, New York, New York 10003, USA

  • *Contact author: mathias.garny@tum.de
  • †Contact author: dominik.laxhuber@tum.de
  • ‡Contact author: rs123@nyu.edu
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Phys. Rev. D 112, 023556 – Published 31 July, 2025

DOI: https://doi.org/10.1103/6zr3-hl4r

Abstract

We apply the framework of Vlasov perturbation theory (VPT) to the two-loop matter power spectrum within Λ cold dark matter cosmologies. The main difference to standard perturbation theory (SPT) arises from taking the velocity dispersion tensor into account, and the resulting screening of the backreaction of UV modes renders loop integrals cutoff independent. VPT is informed about nonperturbative small-scale dynamics via the average value of the dispersion generated by shell-crossing, which impacts the evolution of perturbations on weakly nonlinear scales. When using an average dispersion from halo models, the VPT power spectrum agrees with the one from the simulation, up to differences from missing three-loop contributions. Alternatively, treating the average dispersion as a free parameter we find a remarkably stable prediction of the matter power spectrum from collisionless dynamics at percent level for a wide range of the dispersion scale. We quantify the impact of truncating the Vlasov hierarchy for the cumulants of the phase-space distribution function, finding that the two-loop matter power spectrum is robust to neglecting third and higher cumulants. Finally, we introduce and validate a simplified fast scheme fast VPT that can be easily incorporated into existing codes and is as numerically efficient as SPT.

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Phys. Rev. D 112, 023556– Published 31 July, 2025
  • Received 13 May 2025
  • Accepted 1 July 2025
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