Possible impact of non-Gaussianities on cosmological constraints in neutrino physics

The search for non-Gaussian signatures in the cosmic microwave background (CMB) is crucial for understanding the physics of the early Universe. Given the possibility of non-Gaussian fluctuations in the CMB, a recent revision to the standard $\Lambda$-cold dark matter ($\Lambda \mathrm{CDM}$) model has been proposed, dubbed "super-$\Lambda \mathrm{CDM}$." This model introduces additional free parameters to account for the potential effects of a trispectrum in the primordial fluctuations. In this study, we explore the impact of the super-$\Lambda \mathrm{CDM}$ model on current constraints in neutrino physics. In agreement with previous research, our analysis reveals that, for most of the datasets, the super-$\Lambda \mathrm{CDM}$ parameter $A_0$ significantly deviates from zero at over a 95% confidence level. We then demonstrate that this signal might influence current constraints in the neutrino sector. Specifically, we find that the current constraints on neutrino masses may be relaxed by over a factor of 2 within the super-$\Lambda \mathrm{CDM}$ framework, thanks to the correlation present with $A_0$; such relaxation persists even when we apply constraints to the trispectrum from local measurements, assuming a strong similarity between the two forms. Consequently, locking $A_0=0$ might introduce a bias, leading to overly stringent constraints on the total neutrino mass.