Primordial power spectrum versus extension parameters beyond the standard model
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 Sigma m(p) < 0.48 eV (95% C.L.), the effective number of relativistic species N-eff 4.50 +/- 0.81, and the primordial helium abundance Y-p 0.303 +/- 0.075. The constraints from WMAP7 + SPT + H-0 + BAO are Sigma m(p) < 0.45 eV (95% C.L.), N-eff 3.86 +/- 0.63, and Y-p 0.277 +/- 0.050.