This paper investigates resonant neutrino self-interactions in cosmology by employing, for the first time, the effective field theory of large-scale structure to model their impact on the matter distribution up to mildly nonlinear scales. We explore a broad range of mediator masses in two main analyses; one combining BOSS full shape (FS) galaxy clustering with big bang nucleosynthesis (BBN), and another combining FS with Planck cosmic microwave background (CMB) data. Our results place the strongest cosmological constraints to date on the resonant self-interactions when using $\mathrm{FS}+\mathrm{Planck}$ data, reaching up to $g_{\nu }<10.8\times {10}^{-14}$ at 95% confidence for the 1 eV mediator. Notably, $\mathrm{FS}+\mathrm{BBN}$ can constrain the interaction for the 10 eV mediator independently of CMB data, yielding $g_{\nu }<7.33\times {10}^{-12}$ at 95% confidence. Our results suggest that resonant neutrino self-interactions are unlikely to resolve existing cosmological tensions within the standard $\mathrm{\Lambda }\mathrm{CDM}$ framework.

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• Baryon acoustic oscillations
• Cosmic microwave background
• Cosmological parameters
• Cosmology
• Large scale structure of the Universe
• Hypothetical scalars
• Neutrinos