Classical Nature of the Inflaton Field with Self-Interaction

TL;DR

This paper investigates how self-interaction in the inflaton field influences quantum fluctuations, demonstrating that it facilitates the quantum-to-classical transition essential for understanding primordial universe fluctuations.

Contribution

It provides a detailed analysis of the self-interaction effects on inflaton quantum fluctuations, confirming the quantum-to-classical transition assumption in cosmology.

Findings

Self-interaction drives pure states into mixed statistical ensembles.

Variance of the field matches the expectation value without amplitude change.

Supports the quantum-to-classical transition in primordial fluctuations.

Abstract

Taking into account the effect of self-interaction, the dynamics of the quantum fluctuations of the inflaton field with $\lambda\phi^4$ potential is studied in detail. We find that the self interaction efficiently drives the initial pure state into a mixed one, which can be understood as a statistical ensemble. Further, the expectation value of the squared field operator is found to be converted into the variance of this statistical ensemble without giving any significant change in its amplitude. These results verify the ansatz of the quantum-to-classical transition that has been assumed in the standard evaluation of the amplitude of the primordial fluctuations of the universe.