Classical approximation to quantum cosmological correlations

Abstract

We investigate up to which order quantum effects can be neglected in calculatingcosmological correlation functions after horizon exit. We study, as a toy model,ϕ3 theory on a de Sitter background for a massless minimally coupled scalar fieldϕ. We find that for tree level and one loop contributions in the quantum theory, a goodclassical approximation can be constructed, but for higher loop corrections this isin general not expected to be possible. The reason is that loop corrections getnon-negligible contributions from loop momenta with magnitude up to the Hubble scaleH, at which scale classical physics is not expected to be a good approximation to thequantum theory. An explicit calculation of the one loop correction to the two pointfunction supports the argument that contributions from loop momenta of scaleH are not negligible. Generalization of the arguments for the toy model to derivativeinteractions and the curvature perturbation leads to the conclusion that the leading ordersof non-Gaussian effects generated after horizon exit can be approximated quite well byclassical methods. Furthermore we compare with a theorem of Weinberg. We find thatgrowing loop corrections after horizon exit are not excluded, even in single fieldinflation.