Back reaction of the neutrino field in an Einstein universe

The back-reaction effect of the neutrino field at finite temperature in the background of the static Einstein universe is investigated. A relationship between the temperature of the universe and its radius is found. As in previously studied cases of the massless scalar field and the photon field, this relation exhibits a minimum radius below which no self-consistent solution for the Einstein field equation can be found. A maximum temperature marks the transition from a vacuum-dominated state to the radiation-dominated state universe. In light of the results obtained for the scalar, neutrino and photon fields, the role of the back reaction of quantum fields in controlling the value of the cosmological constant is briefly discussed.