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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.20821 |
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| _version_ | 1866917091607576576 |
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| author | Lee, Nanoom Ali-Haïmoud, Yacine Kamionkowski, Marc |
| author_facet | Lee, Nanoom Ali-Haïmoud, Yacine Kamionkowski, Marc |
| contents | We develop a highly accurate analytic approximation for small-scale non-cold relic perturbations by solving the collisionless Boltzmann equation in the quasi-stationary 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 non-cold relic multipoles with a small set of integral equations solved iteratively. Applying it to massive neutrinos yields a factor-of-two reduction in total runtime relative to CLASSIER without the approximation. Compared to standard CLASS runs (with $\ell_{\rm max}^{\rm NCDM}=40$ 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 wavenumber $k=100\,{\rm Mpc}^{-1}$. 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 non-standard dark-matter models, and offers prospects for further efficiency gains in high-precision cosmological analyses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20821 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient analytic approximation for small-scale non-cold relic perturbations Lee, Nanoom Ali-Haïmoud, Yacine Kamionkowski, Marc Cosmology and Nongalactic Astrophysics We develop a highly accurate analytic approximation for small-scale non-cold relic perturbations by solving the collisionless Boltzmann equation in the quasi-stationary 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 non-cold relic multipoles with a small set of integral equations solved iteratively. Applying it to massive neutrinos yields a factor-of-two reduction in total runtime relative to CLASSIER without the approximation. Compared to standard CLASS runs (with $\ell_{\rm max}^{\rm NCDM}=40$ 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 wavenumber $k=100\,{\rm Mpc}^{-1}$. 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 non-standard dark-matter models, and offers prospects for further efficiency gains in high-precision cosmological analyses. |
| title | Efficient analytic approximation for small-scale non-cold relic perturbations |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2510.20821 |