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 $\Lambda$CDM 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 $\Lambda$ cold dark matter
(CDM) model, i.e. the $w$CDM model with one additional parameter $w$, and the
$w_{0}w_{a}$CDM model with two additional parameters, $w_{0}$ and $w_{a}$. 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 ($H_{0}$). 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 $\Lambda$ is still consistent with
the current data, a phantom dark energy ($w<-1$) or an early phantom dark
energy (i.e. quintom evolving from $w<-1$ to $w>-1$) is slightly more favoured
by current observations, which leads to the fact that in both $w$CDM and
$w_0w_a$CDM models we obtain a larger upper limit of $\sum m_\nu$. We also show
that in the three dark energy models, the constraints on $N_{\rm eff}$ 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 $N_{\rm eff}$. 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.
