We develop a highly accurate analytic approximation for small-scale noncold relic perturbations by solving the collisionless Boltzmann equation in the quasistationary regime. The approximation is implemented in CLASSIER (CLASS Integral Equation Revision), a modified version of the Boltzmann solver CLASS that replaces the traditional truncated Boltzmann hierarchy of noncold relic multipoles with a small set of integral equations solved iteratively. Applying it to massive neutrinos yields a factor-of-two reduction in total run-time relative to CLASSIER without the approximation. Compared to standard CLASS runs (with ${\ell }_{\max }^{\mathrm{NCDM}}=40$ and no late-time massive neutrino fluid approximation) under the same precision setting, CLASSIER with this approximation is faster by a factor of 3–6. The approximation faithfully reproduces the late-time behavior of massive neutrino perturbations and preserves sub-0.1% accuracy in the matter power spectrum today up to comoving wave number $k=100{\mathrm{Mpc}}^{-1}$. With this approximation, massive-neutrino perturbations are no longer the computational bottleneck on small scales for linear-theory predictions. The approach can be readily extendable to nonstandard dark-matter models and offers prospects for further efficiency gains in high-precision cosmological analyses.

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• Cosmology