Cosmic Neutrino Last Scattering Surface

Neutrinos decoupled from the rest of the cosmic plasma when the Universe was less than one second old, far earlier than the photons, which decoupled at $t=380000$ years. Surprisingly, though, the last scattering surface of massive neutrinos is much closer to us than that of the photons. Here we calculate the properties of the last scattering surfaces of the three species of neutrinos.

Figure 1

The comoving distance traveled by a massive neutrino since decoupling until today as a function of mass for two different values of the neutrino momentum. Neutrinos with smaller momenta are traveling more slowly and therefore travel a shorter distance. Note that for masses above ${10}^{-4}\mathrm{eV}$, the neutrino LSS is much closer than that of the CMB.

Figure 2

The probability that a neutrino with mass $m$ last scatters at a given comoving distance from us (the visibility function). Massive neutrinos travel more slowly than massless neutrinos so arrive here from much closer distances. Also shown is the last scattering surface of the cosmic microwave background, virtually indistinguishable from that of an $m_{\nu }={10}^{-4}\mathrm{eV}$ neutrino.

Figure 3

Probability for the distance to the last scattering surface for an electron neutrino with normal hierarchy ($m_2=0.009\mathrm{eV}$; $m_1={10}^{-4}\mathrm{eV}$; $\sin {\theta }_{13}=0$) and degenerate masses ($m_1=m_2=m_3=0.2\mathrm{eV}$).