Classical approximation to quantum cosmological correlations

TL;DR

This paper examines the validity of classical approximations for quantum cosmological correlations, finding they are effective at low loop orders but break down at higher loops due to significant contributions from horizon-scale momenta.

Contribution

It demonstrates that classical methods can approximate leading non-Gaussian effects after horizon exit, but higher loop quantum corrections challenge this approximation.

Findings

Classical approximation works well at tree and one-loop levels.

Higher loop corrections involve non-negligible contributions from horizon-scale momenta.

Growing loop corrections after horizon exit are possible even in single field inflation.

Abstract

We investigate up to which order quantum effects can be neglected in calculating cosmological correlation functions after horizon exit. As a toy model, we study $\phi^3$ theory on a de Sitter background for a massless minimally coupled scalar field $\phi$. We find that for tree level and one loop contributions in the quantum theory, a good classical approximation can be constructed, but for higher loop corrections this is in general not expected to be possible. The reason is that loop corrections get non-negligible contributions from loop momenta with magnitude up to the Hubble scale H, at which scale classical physics is not expected to be a good approximation to the quantum theory. An explicit calculation of the one loop correction to the two point function, supports the argument that contributions from loop momenta of scale $H$ are not negligible. Generalization of the arguments for the toy model to derivative interactions and the curvature perturbation leads to the conclusion that the leading orders of non-Gaussian effects generated after horizon exit, can be approximated quite well by classical methods. Furthermore we compare with a theorem by Weinberg. We find that growing loop corrections after horizon exit are not excluded, even in single field inflation.