Using several cosmological observations , i.e .
the cosmic microwave background anisotropies ( WMAP ) , the weak gravitational lensing ( CFHTLS ) , the measurements of baryon acoustic oscillations ( SDSS+WiggleZ ) , the most recent observational Hubble parameter data , the Union2.1 compilation of type Ia supernovae , and the HST prior , we impose constraints on the sum of neutrino masses ( \sum { m _ { \nu } } ) , the effective number of neutrino species ( N _ { \mathrm { eff } } ) and dark energy equation of state ( w ) , individually and collectively .
We find that a tight upper limit on \sum { m _ { \nu } } can be extracted from the full data combination , if N _ { \mathrm { eff } } and w are fixed .
However this upper bound is severely weakened if N _ { \mathrm { eff } } and w are allowed to vary .
This result naturally raises questions on the robustness of previous strict upper bounds on \sum { m _ { \nu } } , ever reported in the literature .
The best-fit values from our most generalized constraint read \sum { m _ { \nu } } = 0.556 ^ { +0.231 } _ { -0.288 } ~ { } eV , N _ { \mathrm { eff } } = 3.839 \pm 0.452 , and w = -1.058 \pm 0.088 at 68 % confidence level , which shows a firm lower limit on total neutrino mass , favors an extra light degree of freedom , and supports the cosmological constant model .
The current weak lensing data are already helpful in constraining cosmological model parameters for fixed w .
The dataset of Hubble parameter gains numerous advantages over supernovae when w = -1 , particularly its illuminating power in constraining N _ { \mathrm { eff } } .
As long as w is included as a free parameter , it is still the standardizable candles of type Ia supernovae that play the most dominant role in the parameter constraints .