In Big Bang cosmology, neutrino decoupling was the epoch at which neutrinos ceased interacting with other types of matter,[1] and thereby ceased influencing the dynamics of the universe at early times.[2] Prior to decoupling, neutrinos were in thermal equilibrium with protons, neutrons and electrons, which was maintained through the weak interaction. Decoupling occurred approximately at the time when the rate of those weak interactions was slower than the rate of expansion of the universe. Alternatively, it was the time when the time scale for weak interactions became greater than the age of the universe at that time. Neutrino decoupling took place approximately one second after the Big Bang, when the temperature of the universe was approximately 10 billion kelvin, or 1 MeV.[3]
As neutrinos rarely interact with matter, these neutrinos still exist today, analogous to the much later cosmic microwave background emitted during recombination, around 377,000 years after the Big Bang. They form the cosmic neutrino background (abbreviated CνB or CNB). The neutrinos from this event have a very low energy, around 10−10 times smaller than is possible with present-day direct detection. Even high energy neutrinos are notoriously difficult to detect, so the CNB may not be directly observed in detail for many years, if at all. However, Big Bang cosmology makes many predictions about the CNB, and there is very strong indirect evidence that the CNB exists.
Neutrinos are scattered (interfering with free streaming) by their interactions with electrons and positrons, such as the reaction
e-+e+\longleftrightarrow\nue+\bar{\nu}e
The approximate rate of these interactions is set by the number density of electrons and positrons, the averaged product of the cross section for interaction and the velocity of the particles. The number density
n
T
n\proptoT3
\langle\sigmav\rangle\sim
| 2 | |
| G | |
| F |
T2
GF
c
\Gamma
\Gamma=n\langle\sigmav\rangle\sim
| 2 | |
| G | |
| F |
T5
H
H=\sqrt{
| 8\pi | |
| 3 |
G\rho}
where
G
\rho
\rho\proptoT4
| 2 | |
| G | |
| F |
T5\sim\sqrt{GT4}
Solving for temperature gives
T\sim\left(
| \sqrt{G | |
While this is a very rough derivation, it illustrates the important physical phenomena which determined when neutrinos decoupled.
While neutrino decoupling can not be observed directly, it is expected to have left behind a cosmic neutrino background, analogous to the cosmic microwave background radiation of electromagnetic radiation which was emitted at a much later epoch. "The detection of the neutrino background is far beyond the capabilities of the present generation of neutrino detectors."[5] There is data, however, which indirectly indicates the presence of a neutrino background. One piece of evidence is damping of the angular power spectrum of the CMB, which results from anisotropies in the neutrino background.[6]
Another indirect measurement of neutrino decoupling is allowed by the role that neutrino decoupling plays in setting the ratio of neutrons to protons. Before decoupling, the number of neutrons and protons are maintained in their equilibrium abundances by weak interactions, specifically beta decay and electron capture (or inverse beta decay) according to
n\leftrightarrowp+e-+\bar{\nu}e
and
p+e-\leftrightarrow\nue+n
Once the rate of weak interactions is slower than the characteristic rate of the expansion of the universe, this equilibrium cannot be maintained, and the abundance of neutrons to protons "freezes in," at a value
| \left[ | n |
| n+p |
\right]=0.21
This value is simply found by evaluating the Boltzmann factor for neutrons and protons at decoupling time, according to
| nn(T) | |
| np(T) |
=\exp\left(
| -\Deltam | |
| T |
\right)
where
\Deltam
T
Big Bang cosmology makes many predictions about the CNB, 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). It is well known that the CMB has irregularities. Some of the CMB fluctuations were roughly regularly spaced, because of the effect of baryon acoustic oscillations. In theory, the decoupled neutrinos should have had a very slight effect on the phase of the various CMB fluctuations.[10]
In 2015, it was reported that such shifts had been detected in the CMB. Moreover, the fluctuations corresponded to neutrinos of almost exactly the temperature predicted by Big Bang theory (compared to a prediction of 1.95 K), and exactly three types of neutrino, the same number of neutrino flavours currently predicted by the Standard Model.[10]