Strong constraints on a simple self-interacting neutrino cosmology

Some cosmic microwave background (CMB) data allow a cosmological scenario in which the free streaming of neutrinos is delayed until close to matter-radiation equality. Interestingly, recent analyses have revealed that large-scale structure (LSS) data also align with this scenario, discarding the possibility of an accidental feature in the CMB sky and calling for further investigation into the free-streaming nature of neutrinos. By assuming a simple representation of self-interacting neutrinos, we investigate whether this nonstandard scenario can accommodate a consistent cosmology for both the CMB power spectra and the large-scale distribution of galaxies simultaneously. Employing three different approaches - a profile likelihood exploration, a nested sampling method, and a heuristic Metropolis-Hasting approximation - we exhaustively explore the parameter space and demonstrate that galaxy data exacerbates the challenge already posed by the Planck polarization data for this nonstandard scenario. We find that the Bayes factor disfavor strong interactions among neutrinos over the $\Lambda$CDM and $\Lambda$CDM + $N_\mathrm{eff}$ + $\sum m_\nu$ models with odds of $7:10000$ and $23:1000$, respectively, providing large evidence against the simple self-interacting neutrino model. Our analysis emphasizes the need to consider a broader range of phenomenologies in the early Universe. We also highlight significant numerical and theoretical challenges ahead in uncovering the exact nature of the feature observed in the data or, ultimately, confirming the standard chronological evolution of the Universe.