Pseudoscalar sterile neutrino self-interactions in light of Planck, SPT and ACT data

We reassess the viability of a cosmological model including a fourth additional sterile neutrino species that self-interacts through a new pseudoscalar degree of freedom. We perform a series of extensive analyses fitting various combinations of cosmic microwave background (CMB) data from Planck, the Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT), both alone and in combination with Baryon Acoustic Oscillation (BAO) and Supernova Ia (SnIa) observations. We show that the scenario under study, although capable to resolve the Hubble tension without worsening the so-called $S_8$ tension about the growth of cosmic structures, is severely constrained by high-multipole polarization data from both Planck and SPT. Intriguingly, when trading Planck TE-EE data for those from ACT, we find a $\gtrsim 3 \sigma$ preference for a non-zero sterile neutrino mass, $m_s=3.6^{+1.1}_{-0.6}$ eV (68 % C.L.), compatible with the range suggested by longstanding short-baseline (SBL) anomalies in neutrino oscillation experiments. The pseudoscalar model provides indeed a better fit to ACT data compared to $\Lambda$CDM ($\Delta\chi^2 \simeq -5$, $\Delta \rm{AIC}=-1.3$), although in a combined analysis with Planck the $\Lambda$CDM model is still favoured, as the preference for a non-zero sterile neutrino mass is mostly driven by ACT favouring a higher value for the primordial spectral index $n_s$ with respect to Planck. We show that the mild tension between Planck and ACT is due to the different pattern in the TE and EE power spectra on multipoles between $350 \lesssim \ell \lesssim 1000$. We also check the impact of marginalizing over the gravitational lensing information in Planck data, showing that the model does not solve the CMB lensing anomaly. Future work including higher precision data from current and upcoming CMB ground-based experiments will be crucial to test these results.