Cosmological search for sterile neutrinos after Planck 2018
  Sterile neutrinos can affect the evolution of the universe, and thus using
the cosmological observations can search for sterile neutrinos. In this work,
we use the cosmic microwave background (CMB) anisotropy data from the Planck
2018 release, combined with the latest baryon acoustic oscillation (BAO), type
Ia supernova (SN), and Hubble constant ($H_0$) data, to constrain the
cosmological models with considering sterile neutrinos. In order to test the
influences of the properties of dark energy on the {results} of searching for
sterile neutrinos, in addition to the $\Lambda$ cold dark matter ($\Lambda$CDM)
model, we also consider the $w$CDM model and the holographic dark energy (HDE)
model. We find that the existence of sterile neutrinos {is not preferred} when
the $H_0$ local measurement is not included in the data combination. When the
$H_0$ measurement is included in the joint constraints, it is found that
$\Delta N_{\rm eff}>0$ is {favored} at about 2.7$\sigma$ level for the
$\Lambda$CDM model and at about 1-1.7$\sigma$ level for the $w$CDM model.
However, $m_{\nu,{\rm{sterile}}}^{\rm{eff}}$ still cannot be well constrained
and only upper limits can be given. In addition, we find that the HDE model is
definitely ruled out by the current data. We also discuss the issue of the
Hubble tension, and we conclude that involving sterile neutrinos in the
cosmological models cannot truly resolve the Hubble tension.
