Classical approximation to quantum cosmological correlations

TL;DR

This work interrogates the boundary between classical and quantum descriptions for cosmological correlators generated after horizon exit, using a toy $\phi^3$ theory on exact de Sitter space. It demonstrates that tree-level and one-loop quantum contributions can be well approximated by classical evolution, but higher-loop corrections receive non-negligible input from loop momenta up to the Hubble scale $H$, complicating a purely classical picture. The authors extend these insights to derivative interactions and the curvature perturbation $\zeta$, showing that leading non-Gaussian effects after horizon exit are accessible classically at leading order and, up to one loop with a suitable cutoff, may be captured as well; however, growing loop corrections remain a possibility even in single-field inflation, in line with Weinberg's results. The analysis clarifies when stochastic or classical methods are reliable and highlights the special role of $H$-scale physics in de Sitter cosmology, with implications for interpreting primordial non-Gaussianity in multifield scenarios.

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 $φ^3$ theory on a de Sitter background for a massless minimally coupled scalar field $φ$. 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.