Neutrino decoupling

In Big Bang cosmology, neutrino decoupling refers to the epoch at which neutrinos ceased interacting with baryonic matter, and thereby ceased influencing the dynamics of the universe at early times. 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 kelvins, or 1 MeV. In Big Bang cosmology, neutrino decoupling refers to the epoch at which neutrinos ceased interacting with baryonic matter, and thereby ceased influencing the dynamics of the universe at early times. 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 kelvins, or 1 MeV. 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 CvB 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 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 {displaystyle n} of the relativistic electrons and positrons depends on the cube of the temperature T {displaystyle T} , so that n ∝ T 3 {displaystyle npropto T^{3}} . The product of the cross section and velocity for weak interactions for temperatures (energies) below W/Z boson masses (~100 GeV) is given approximately by ⟨ σ v ⟩ ∼ G F 2 T 2 {displaystyle langle sigma v angle sim G_{F}^{2}T^{2}} , where G F {displaystyle G_{F}} is Fermi's constant (as is standard in particle physics calculations, factors of the speed of light c {displaystyle c} are set equal to 1). Putting it all together, the rate of weak interactions Γ {displaystyle Gamma } is This can be compared to the expansion rate which is given by the Hubble parameter H {displaystyle H} , with where G {displaystyle G} is the gravitational constant and ρ {displaystyle ho } is the energy density of the universe. At this point in cosmic history, the energy density is dominated by radiation, so that ρ ∝ T 4 {displaystyle ho propto T^{4}} . As the rate of weak interaction depends more strongly on temperature, it will fall more quickly as the universe cools. Thus when the two rates are approximately equal (dropping terms of order unity, including an effective degeneracy term which counts the number of states of particles which are interacting) gives the approximate temperature at which neutrinos decouple: