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 _ { 0 } w _ { 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 _ { 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 _ { eff } .
Therefore , we conclude that the dark energy parameters can exert a significant influence on the cosmological weighing of neutrinos , but almost can not affect the constraint on dark radiation .