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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 the previously studied cases of the massless scalar field and the photon field, this relation exhibit 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 statedoi:10.1088/0264-9381/20/2/306 fatcat:ngpeb3et3rhbnluo3h46n3s4jy