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Emergent Dark Energy, neutrinos and cosmological tensions

The Phenomenologically Emergent Dark Energy model, a dark energy model with the same number of free parameters as the flat $Λ$CDM, has been proposed as a working example of a minimal model which can avoid the current cosmological tensions. A straightforward question is whether or not the inclusion of massive neutrinos and extra relativistic species may spoil such an appealing phenomenological alternative. We present the bounds on $M_ν$ and $N_{\rm eff}$ and comment on the long standing $H_0$ and $σ_8$ tensions within this cosmological framework with a wealth of cosmological observations. Interestingly, we find, at $95\%$ confidence level, and with the most complete set of cosmological observations, $M_ν\sim 0.21^{+0.15}_{-0.14}$ eV and $N_{\rm eff}= 3.03\pm 0.32$ i.e. an indication for a non-zero neutrino mass with a significance above $2σ$. The well known Hubble constant tension is considerably easened, with a significance always below the $2σ$ level.