A Thermal Neutrinos: Detecting Ancient Particles in the Universe?

[Cato]

Would neutrinos emitted in the distant and early universe be slowed enough to become thermal neutrinos? Could these be detected?

 

[mfb]

The cosmic neutrino background should be thermal. PTOLEMY is a plan to measure it.

Neutrinos emitted by nuclear processes after the big bang are not thermal, even if they become slow in the very distant future their energy spectrum will look different.

 

[Cato]

The cosmic neutrino background should be thermal. PTOLEMY is a plan to measure it.

Neutrinos emitted by nuclear processes after the big bang are not thermal, even if they become slow in the very distant future their energy spectrum will look different.

Do the cosmic background neutrinos remain in thermal equilibrium by interacting with matter? Or are they thermal simply because of the effects of expansion?

 

[George Jones]

Do the cosmic background neutrinos remain in thermal equilibrium by interacting with matter? Or are they thermal simply because of the effects of expansion?

The latter.

Before decoupling, neutrinos were in thermal equilibrium with the "cosmic soup". It can be shown that after decoupling, expansion of the universe redshifts a thermal spectrum for radiation into a thermal spectrum. Weinberg in his book "Cosmology" demonstrates his on pages 101-102. Weinberg

Thus the photon density has been given a black-body form even after hye photons went out of equilibrium with matter, but with a redshifted temperature.

The above applies to massless neutrinos, which is a good approximation for some of the history of the universe. Their non-zero masses, however, gradually shift their spectrum away from a thermal spectrum. From "Relativistic Cosmology" by Ellis, Maartens, and MacCallum page 304:

The most massive neutrinos become non-relativistic well after radiation matter inequality. We can estimate the non-relativistic redshift by setting the mean energy per neutrino equal to the mass.

 

[Cato]

Terrific. Thanks very much.