Searching for sterile neutrinos in dynamical dark energy cosmologies

We investigate how the dark energy properties change the cosmological limits on sterile neutrino parameters by using recent cosmological observations. We consider the simplest dynamical dark energy models, the $w$CDM model and the holographic dark energy (HDE) model, to make an analysis. The cosmological observations used in this work include the Planck 2015 CMB temperature and polarization data, the baryon acoustic oscillation data, the type Ia supernova data, the Hubble constant direct measurement data, and the Planck CMB lensing data. We find that, $m_{\nu,{\rm{sterile}}}^{\rm{eff}}<0.2675$ eV and $N_{\rm eff}<3.5718$ for $\Lambda$CDM cosmology, $m_{\nu,{\rm{sterile}}}^{\rm{eff}}<0.5313$ eV and $N_{\rm eff}<3.5008$ for $w$CDM cosmology, and $m_{\nu,{\rm{sterile}}}^{\rm{eff}}<0.1989$ eV and $N_{\rm eff}<3.6701$ for HDE cosmology, from the constraints of the combination of these data. Thus, without the addition of measurements of growth of structure, only upper limits on both $m_{\nu,{\rm{sterile}}}^{\rm{eff}}$ and $N_{\rm eff}$ can be derived, indicating that no evidence of the existence of a sterile neutrino species with eV-scale mass is found in this analysis. Moreover, compared to the $\Lambda$CDM model, in the $w$CDM model the limit on $m_{\nu,{\rm{sterile}}}^{\rm{eff}}$ becomes much looser, but in the HDE model the limit becomes much tighter. Therefore, the dark energy properties could significantly influence the constraint limits of sterile neutrino parameters.