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astro-ph.CO

Why does cosmic structure theory break down, and can the Zel'dovich trick fix it?

Svetlin V. Tassev

May 27, 2026

Standard perturbative expansions for cosmic structure growth fail not because perturbations are too large, but because mathematicians' dominated-convergence theorem is violated—infinite sums and integrals get swapped in an illegal way. Tassev shows this obstruction limits both Eulerian and Lagrangian approaches, and proposes sidestepping it entirely: evolve phase-space statistics using the BBGKY hierarchy initialized with Zel'dovich initial conditions, avoiding the expansion that causes trouble. The bottleneck—numerically computing Zel'dovich correlators—is now solved.
Published as Dominated-Convergence Failure in Cosmological Perturbation Theory and a Numerical Foundation for BBGKY+ZA arXiv:2605.28943
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