Constraining neutrino mass and extra relativistic degrees of freedom in dynamical dark energy models using Planck 2015 data in combination with low-redshift cosmological probes: basic extensions to ΛCDM cosmology

We investigate how the properties of dark energy affect the cosmological measurements of neutrino mass and extra relativistic degrees of freedom. We limit ourselves to the most basic extensions of cold dark matter (CDM) model, i. e. the wCDM model with one additional parameter w, and the w₀w₀CDM model with two additional parameters, w₀ and w₀. In the cosmological fits, we employ the 2015 cosmic microwave background temperature and polarization data from the Planck mission, in combination with low-redshift measurements such as the baryon acoustic oscillations, Type Ia supernovae and the Hubble constant (H₀). Given effects of massive neutrinos on large-scale structure, we further include weak lensing, redshift space distortion, Sunyaev--Zeldovich cluster counts and Planck lensing data. We show that, though the cosmological constant is still consistent with the current data, a phantom dark energy (w-1) is slightly more favoured by current observations, which leads to the fact that in both wCDM and w₀wₐCDM models we obtain a larger upper limit of m_. We also show that in the three dark energy models, the constraints on N ₄₅₅ are in good accordance with each other, all in favour of the standard value 3. 046, which indicates that the dark energy parameters almost have no impact on constraining N ₄₅₅. Therefore, we conclude that the dark energy parameters can exert a significant influence on the cosmological weighing of neutrinos, but almost cannot affect the constraint on dark radiation.