Revisit the possibility of solving the Hubble tension with Neff

The [Formula: see text]CDM model is considered as a standard model because of its self-consistency in theory and nearly perfect fitting to most cosmological observation. However, in recent years, the so-called “Hubble tension”, which means the discrepancy between the early- and late-time observations of Hubble constant [Formula: see text], has been more and more prominent. Based on the previous research, we update the data combination with Planck 2018 and BAO, detect the relationship of Hubble constant and effective number of relativistic species [Formula: see text], then revisit the possibility of solving Hubble tension starting from [Formula: see text]. Considering a class of [Formula: see text] models with fixed values of [Formula: see text], a linear relationship of [Formula: see text] and [Formula: see text] is presented as [Formula: see text] [Formula: see text], which indicates that Hubble tension would be solved thoroughly if [Formula: see text]. The numerical results of model with fixed [Formula: see text] show that the Hubble tension is reduced to [Formula: see text]. However, the [Formula: see text]CDM model is still preferred over other models, especially over the model with [Formula: see text] by [Formula: see text]. In brief, it is unlikely to solve the Hubble tension by varying [Formula: see text] alone.