We present the first search for evidence of neutrino self-interaction with two new, state-of-the-art likelihoods for eBOSS Lyman-$\alpha$ data. These are an effective field theory (EFT) likelihood with priors from the Sherwood simulation suite, and a compressed likelihood derived from an emulator built using the PRIYA simulation suite. Previous analyses that combined Planck measurements with eBOSS Lyman-$\alpha$ likelihoods based on earlier simulations found a preference for neutrino self-interactions. In contrast, using either of the new eBOSS Lyman-$\alpha$ likelihoods, we find that a joint analysis with the cosmic microwave background data from Planck prefers a negligible level of neutrino self-interaction, and derive new constraints on the neutrino self-coupling: ${\log }_{10}(G_{\mathrm{eff}}{\mathrm{MeV}}^2)=-5.57_{-0.58}^{+0.98}$ for $Planck+\mathrm{EFT}$ Lyman-$\alpha$, and ${\log }_{10}(G_{\mathrm{eff}}{\mathrm{MeV}}^2)=-5.16_{-0.67}^{+1.12}$ for $Planck+\mathrm{PRIYA}$ Lyman-$\alpha$, at 68% confidence. We also consider Planck in combination with DESI BAO data, and find that the latter does not provide significant constraining power for neutrino self-interactions.

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• Cosmic microwave background
• Cosmological parameters
• Dark matter
• Large scale structure of the Universe