Classical Nature of the Inflaton Field with Self-Interaction

Taking into account the effect of self-interaction, the dynamics of thequantum fluctuations of the inflaton field with $\lambda\phi^4$ potential isstudied in detail. We find that the self interaction efficiently drives theinitial pure state into a mixed one, which can be understood as a statisticalensemble. Further, the expectation value of the squared field operator is foundto be converted into the variance of this statistical ensemble without givingany significant change in its amplitude. These results verify the ansatz of thequantum-to-classical transition that has been assumed in the standardevaluation of the amplitude of the primordial fluctuations of the universe.Comment: 23 pages, submitted to Phys. Rev. D1