Determining Neutrino Mass from the Cosmic Microwave Background Alone

Distortions of cosmic microwave background temperature and polarization maps caused by gravitational lensing, observable with high angular resolution and high sensitivity, can be used to measure the neutrino mass. Assuming two massless species and one with mass $m_{\nu }$, we forecast $\sigma (m_{\nu })=0.15\mathrm{e}\mathrm{V}$ from the Planck satellite and $\sigma (m_{\nu })=0.04\mathrm{e}\mathrm{V}$ from observations with twice the angular resolution and $\sim 20$ times the sensitivity. A detection is likely at this higher sensitivity since the observation of atmospheric neutrino oscillations requires $\Delta m_{\nu }^2\gtrsim (0.04\mathrm{e}\mathrm{V}{)}^2$.