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In this work, for the first time in literature, we compare the predictions ofnon-minimally coupled Natural and Coleman-Weinberg potentials in the $n_s-r$plane against the constraints from the latest cosmological data in an extended$\Lambda$CDM model where we include non-standard self-interactions amongmassive neutrinos, mediated by a heavy scalar or vector boson. For theinflationary potentials, we consider two different formulations in gravity thatare non-minimally coupled to the scalar field of the inflaton: \textit{Metricand Palatini.} We only consider the self-interaction to be present among$\tau$-neutrinos and only at moderate strengths. This is because stronginteractions among $\tau$-neutrinos, or any strength self-interaction amongelectron- and muon-neutrinos, as well as any strength flavor-universalinteractions, are strongly disfavoured from particle physics experiments.  In terms of cosmological data, we use the latest public CMB datasets fromPlanck and BICEP/Keck collaborations, along with other data from CMB lensing,BAO, RSD, and SNe Ia luminosity distance measurements. We find that there aresome situations where predictions from the inflationary models are ruled out atmore than 2$\sigma$ by the minimal $\Lambda$CDM$+r$ model, but they are allowedin the self-interacting neutrino scenario.

First constraints on Non-minimally coupled Natural and Coleman-Weinberg  inflation in the light of massive neutrino self-interactions and  Planck+BICEP/Keck