We reconstruct the shape of the primordial power spectrum of curvature perturbations in extended cosmological models , including addition of massive neutrinos , extra relativistic species or varying primordial helium abundance , from the latest cosmic microwave background data from the Wilkinson Microwave Anisotropy Probe , the Atacama Cosmology Telescope and the South Pole Telescope .
We find that a scale-invariant primordial spectrum is disfavored by the data at 95 % confidence level even in the presence of massive neutrinos , however it can lie within the 95 % confidence region if the effective number of relativistic species or the primordial helium abundance is allowed to vary freely .
The constraints on the extension parameters from WMAP7+ACT+ H _ { 0 } +BAO , are the total mass of neutrinos \sum m _ { \nu } < 0.48 eV ( 95 % CL ) , the effective number of relativistic species N _ { eff } = 4.50 \pm 0.81 and the primordial helium abundance Y _ { p } = 0.303 \pm 0.075 .
The constraints from WMAP7+SPT+ H _ { 0 } +BAO , are \sum m _ { \nu } < 0.45 eV ( 95 % CL ) , N _ { eff } = 3.86 \pm 0.63 and Y _ { p } = 0.277 \pm 0.050 .