Classical approximation to quantum cosmological correlations

Details Classical approximation to quantum cosmological correlations Classical approximation to quantum cosmological correlations

2007-07-05

arxiv.org/abs/0707.0842v3

JCAP0711:023,2007

Physics

High Energy Physics

High Energy Physics - Theory

44 pages, 1 figure; v2: corrected errors, added references, conclusions unchanged; v3: added section in which we compare with

Scientific paper

10.1088/1475-7516/2007/11/023

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.

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