Search for sterile neutrinos in holographic dark energy cosmology:
  Reconciling Planck observation with the local measurement of the Hubble
  constant
  We search for sterile neutrinos in the holographic dark energy cosmology by
using the latest observational data. To perform the analysis, we employ the
current cosmological observations, including the cosmic microwave background
temperature power spectrum data from the Planck mission, the baryon acoustic
oscillation measurements, the type Ia supernova data, the redshift space
distortion measurements, the shear data of weak lensing observation, the Planck
lensing measurement, and the latest direct measurement of $H_0$ as well. We
show that, compared to the $\Lambda$CDM cosmology, the holographic dark energy
cosmology with sterile neutrinos can relieve the tension between the Planck
observation and the direct measurement of $H_0$ much better. Once we include
the $H_0$ measurement in the global fit, we find that the hint of the existence
of sterile neutrinos in the holographic dark energy cosmology can be given.
Under the constraint of the all-data combination, we obtain $N_{\rm eff}=
3.76\pm0.26$ and $m_{\nu,\rm sterile}^{\rm eff}< 0.215\,\rm eV$, indicating
that the detection of $\Delta N_{\rm eff}>0$ in the holographic dark energy
cosmology is at the $2.75\sigma$ level and the massless or very light sterile
neutrino is favored by the current observations.
