TITLE:
Collisionless Kinetic Resonances in Open Cosmological Voids
AUTHORS:
Nikolay N. Fimin
KEYWORDS:
Cosmological Voids, Collisionless Dark Matter, Vlasov-Poisson-Λ Model, Kinetic Resonances, Phase-Space Dynamics, Large-Scale Structure
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.9,
September
10,
2026
ABSTRACT: Cosmological voids are underdense regions whose late-time evolution is controlled by expansion, tidal environment and boundary flows. We treat a void as an open collisionless dark-matter cell, where “collisionless” means that two-body encounters are neglected and “open” means that the phase-space trajectories generated by the transport equation (the kinetic characteristics) may cross the cell boundary, governed by the local Newtonian Vlasov-Poisson system—collisionless phase-space transport coupled self-consistently to Newtonian Poisson gravity—with cosmological constant Λ. The central object is the self-consistent linear Vlasov response resolvent, i.e. the inverse of the coupled linear frequency-domain response operator wherever that inverse exists, obtained by combining transport along the stationary-reference characteristics with the Newtonian Poisson response. For complex frequency
ω∈ℂ
, it is analytically continued from the upper frequency half-plane
Imω>0
across the continuous van Kampen spectrum, i.e. the continuum of characteristic transport frequencies. In gravity-dominated cells the response remains associated with reversible phase mixing, understood as dephasing along bounded or mixed characteristics. In the asymptotic void regime, however, the Hessian
ℋ=∇∇Ψ
(the matrix of second derivatives of the effective potential Ψ) has three negative eigenvalues, and the characteristic flow becomes hyperbolic, meaning that nearby trajectories separate exponentially. For perturbations belonging to a Sedláček-type analytic test class, defined by momentum-strip analyticity together with derivative bounds and decay, this geometry permits continuation of the projected resolvent to the lower half-plane, where isolated poles whose generalized modes carry flux away from the cell define Gamow-like kinetic resonances. Projection on the dominant expanding characteristic reduces the spatial response to a Weber, or parabolic-cylinder, equation; finite cosmic-web cell boundaries regularise the outgoing modes by truncating their formal spatial growth, while the leading projected inverted-oscillator model defines a discrete resonance lattice. The exact equal spacing belongs to this projected Weber normal form—the leading quadratic one-channel representative—rather than to the full six-dimensional self-consistent Fredholm determinant, i.e. the determinant of identity minus the response operator. Pole dominance—long-time dominance of pole residues over the continued-spectrum remainder—is conditional on the analytic and decay assumptions stated below. The fundamental mode gives a characteristic void-clearing rate and implies a kinetic outflow scaling proportional to
ρ
∂
λ
*
3/2
R
5
, where
ρ
∂
is a characteristic boundary mass density,
λ
*
>0
is the negative of the most negative Hessian eigenvalue, and
R
is the characteristic cell radius. The framework is proposed as a continuum theoretical model for resonant relaxation (pole-controlled decay), phase-space leakage (transport across the cell boundary) and kinematic memory (persistent velocity or phase-space signatures) in large cosmological voids, with possible observational diagnostics in void density profiles, cell-frame velocity gradients and boundary anisotropies.