  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+H0+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 +/- 0.81 and the primordial helium abundance
Y_p = 0.303 +/- 0.075. The constraints from WMAP7+SPT+H0+BAO, are sum(m_nu) <
0.45 eV (95% CL), N_eff = 3.86 +/- 0.63 and Y_p = 0.277 +/- 0.050.
