by the same process of cosmic expansion, from the same starting temperature. However, when the temperature dropped below double the mass of the electron, most electrons and positrons annihilated, transferring their heat and entropy to photons, thus increasing the temperature of the photons. So the ratio of the temperature of the photons before and after the electron–positron annihilation is the same as the ratio of the temperature of the neutrinos and the photons in the current Regime 2. To find this ratio, we assume that the entropy of the universe was approximately conserved by the electron–positron annihilation. Then using where is the effective number of degrees of freedom and is the plasma or photon temperature. Once reactions cease, the entropy should remain approximately "stuck" for all temperatures below the cut-off temperature, and we find that Here denotes the lowest temperature where pair production and annihilation were in equilibrium; and denotes the temperature after the temperature fell below the regime-shift temperature , after the remaining, but no longer refreshed, electron–positron pairs had annihilated and contributed to the total photon energy. The related temperatures and are the simultaneous temperatures of the photons () and neutrinos () respectively, whose ratio stays "stuck" at the same value indefinitely, after The factor is determined by a sum, based on the particle species engaged in the original equilibrium reaction: + 2 for each photon (or other massless bosons, if any). + for each electron, positron, or other fermion. Whereas the factor is simply 2, since the present regime only concerns photons, in thermal equilibrium with at most themselves. So Since the cosmic photon background temperature at present has cooled to it follows that the neutrino background temperature is currently The above discussion is technically valid for massless neutrinos, which are always relativistic. For neutrinos with a non-zero rest mass, at low temperature where the neutrinos become non-relativistic, a description in terms of a temperature is not appropriate. In other words, when the neutrinos' thermal energy ( is the Boltzmann constant) falls below the rest mass energy in a low-temperature case one should instead speak of the neutrinos' collective energy density, which remains both relevant and well-defined. Indirect evidence for the CB Relativistic neutrinos contribute to the radiation energy density of the universe , typically parameterized in terms of the effective number of neutrino species : where denotes the redshift. The first term in the square brackets