Abstract
One hundred years ago, because the mass of galaxies estimated was much more than the mass of observable objects, scientists proposed that there should be more matter hidden in the dark, called it as dark matter. However, until now, no one found it yet. More and more hypotheses about the materials of dark matter have been proposed and discussed. The hypothesis of weakly interacting massive particles is the lead candidate. Instead of assuming non-observable particles, such as sterile neutrinos and neutralinos, we would like to investigate dark matter based neutrinos (vᵤ, vₑ and v˕), which are stable and have only weak interactions. As the only detected weakly interacting particles in the lab, neutrinos become the leading role of this thesis. According to the theory proposed by Lee and Yang in 1955, apart from four fundamental interactions, we derive a new force in a generalized U(1) group based on the conservation law of the lepton number. It is called as the lepton force. It turns out to be a constant force between two point lepton charges. However, in our mathematical model, the size of objects cannot be neglected. For convenience, we model the universe as a gigantic sphere with uniform lepton charges (carried by the electrons in atoms). We calculate the effective force of this sphere on a point lepton charge pf a neutrino. Our calculations show that we may consider the lepton charges of the gigantic sphere as concentrated at the center of the sphere. The new force formula is linear and will increase as the distance increases. Based on the hadron decay result, the number of neutrinos are much more than the numbers of protons and electrons which are the main particles of the observable universe. However, it is difficult to detect neutrinos in nature. This result suggests that our hypothesis may be consistent with observation of dark matter. The only problem is that energy of the original neutrinos is too high so that they cannot make up dark matter. But dark matter can consists of non-relativistic neutrinos. We can obtain the lepton potential with the lepton force. Based on the energy conservation law, neutrinos will move slower as the distance increases. And according to the simulation result, neutrinos will cold down to non-relativistic particles even stop somewhere inside the observable universe.