Constraining neutrino masses by CMB experiments alone

It is shown that a subelectronvolt upper limit can be derived on the neutrino mass from the cosmic microwave background (CMB) data alone in the ΛCDM model with the power-law adiabatic perturbations, without the aid of any other cosmological data. Assuming the flatness of the Universe, the constraint we can derive from the current Wilkinson Microwave Anisotropy Probe observations is ∑m_ν<2.0  eV at the 95% confidence level for the sum over three species of neutrinos (m_ν<0.66  eV for the degenerate neutrinos) by maximizing the likelihood over six other cosmological parameters. This constraint modifies little even if we abandon the flatness assumption for the spatial curvature. We argue that it would be difficult to improve the limit much beyond ∑m_ν≲1.5  eV using only the CMB data, even if their statistics are substantially improved. However, a significant improvement of the limit is possible if an external input is introduced that constrains the Hubble constant from below. The parameter correlation and the mechanism of CMB perturbations that give rise to the limit on the neutrino mass are also elucidated.