Constraints on secret neutrino interactions after Planck

(Abridged) Neutrino interactions beyond the standard model may affect the cosmological evolution and can be constrained through observations. We consider the possibility that neutrinos possess secret scalar or pseudoscalar interactions mediated by the Nambu-Goldstone boson of a still unknown spontaneously broken global $U(1)$ symmetry, as in, e.g. , Majoron models. In such scenarios, neutrinos still decouple at $T\simeq 1$ MeV, but become tightly coupled again ('recouple') at later stages of the cosmological evolution. We use available observations of CMB anisotropies, including Planck 2013 and the joint BICEP2/Planck 2015 data, to derive constraints on the quantity $\gamma_{\nu \nu}^4$, parameterizing the neutrino collision rate due to (pseudo)scalar interactions. We consider both a minimal extension of the standard $\Lambda$CDM model, and scenarios with extra relativistic species or non-vanishing tensors. We find a typical constraint $\gamma_{\nu \nu}^4 < 0.9\times 10^{-27}$ (95% C.L.), implying an upper limit on the redshift $z_{rec}$ of neutrino recoupling $< 8500$. In the framework of Majoron models, the upper limit on $\gamma_{\nu \nu}$ roughly translates on a constraint $g < 8.2\times 10^{-7}$ on the Majoron-neutrino coupling constant $g$. In general, the data show a weak ($\sim 1\sigma$) but intriguing preference for non-zero values of $\gamma_{\nu \nu}^4$, with best fits in the range $\gamma_{\nu \nu}^4 = (0.15 - 0.35)\times 10^{-27}$, depending on the particular dataset. This is more evident when either observations from ACT and SPT are included, or the possibility of non-vanishing tensor modes is considered. In particular, for the minimal model $\Lambda$CDM +$\gamma_{\nu \nu}$ and including the Planck 2013, ACT and SPT data, we report $\gamma_{\nu \nu}^4=( 0.45^{+0.15}_{-0.38} )\times10^{-27}$ ($200 < z_{rec} < 5700$) at 68% confidence level.