To find this ratio, we assume that the entropy s of the universe was approximately conserved by the electron–positron annihilation.
, after the remaining, but no longer refreshed, electron–positron pairs had annihilated and contributed to the total photon energy.
are the simultaneous temperatures of the photons (γ) and neutrinos (ν) respectively, whose ratio stays "stuck" at the same value indefinitely, after
is determined by a sum, based on the particle species engaged in the original equilibrium reaction: Whereas the factor
in a low-temperature case one should instead speak of the neutrinos' collective energy density, which remains both relevant and well-defined.
The Standard Model with its three neutrino species predicts a value of Nν ≃ 3.046,[5] including a small correction caused by a non-thermal distortion of the spectra during e+×e− annihilation.
The radiation density had a major impact on various physical processes in the early universe, leaving potentially detectable imprints on measurable quantities, thus allowing us to infer the value of Nν from observations.
Due to its effect on the expansion rate of the universe during Big Bang nucleosynthesis (BBN), the theoretical expectations for the primordial abundances of light elements depend on Nν.
Astrophysical measurements of the primordial 4He and 2D abundances lead to a value of Nν = 3.14+0.70−0.65 at 68% c.l.,[6] in very good agreement with the Standard Model expectation.
The presence of the CνB affects the evolution of CMB anisotropies as well as the growth of matter perturbations in two ways: Due to its contribution to the radiation density of the universe (which determines for instance the time of matter–radiation equality), and due to the neutrinos' anisotropic stress which dampens the acoustic oscillations of the spectra.
Additionally, free-streaming massive neutrinos suppress the growth of structure on small scales.
The WMAP spacecraft's five-year data combined with type Ia supernova data and information about the baryon acoustic oscillation scale yielded Nν = 4.34+0.88−0.86 at 68% c.l.,[7] providing an independent confirmation of the BBN constraints.
The Planck spacecraft collaboration has published the tightest bound to date on the effective number of neutrino species, at Nν = 3.15±0.23.
[8] Big Bang cosmology makes many predictions about the CνB, and there is very strong indirect evidence that the cosmic neutrino background exists, both from Big Bang nucleosynthesis predictions of the helium abundance, and from anisotropies in the cosmic microwave background.
One of these predictions is that neutrinos will have left a subtle imprint on the cosmic microwave background (CMB).
Some of the CMB fluctuations were roughly regularly spaced, because of the effect of baryon acoustic oscillation.
In theory, the decoupled neutrinos should have had a very slight effect on the phase of the various CMB fluctuations.
[1][2] Confirmation of the existence of these relic neutrinos may only be possible by directly detecting them using experiments on Earth.
This will be difficult as the neutrinos which make up the CνB are non-relativistic, in addition to interacting only weakly with normal matter, and so any effect they have in a detector will be hard to identify.
One proposed method of direct detection of the CνB is to use the capture of cosmic relic neutrinos on tritium i.e. 3H, leading to an induced form of beta decay.