Resummation of infrared logarithms in de Sitter space via Dyson-Schwinger equations: The ladder-rainbow approximation

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Abstract
We study the infrared (large separation) behavior of a massless minimally coupled scalar quantum field theory with a quartic self interaction in de Sitter spacetime. We show that the perturbation series in the interaction strength is singular and secular, i.e. it does not lead to a uniform approximation of the solution in the infrared region. Only a nonperturbative resummation can capture the correct infrared behavior. We seek to justify this picture using the Dyson-Schwinger equations in the ladder-rainbow approximation. We are able to write down an ordinary differential equation obeyed by the two-point function and perform its asymptotic analysis. Indeed, while the perturbative series—truncated at any finite order—is growing in the infrared, the full nonperturbative sum can be decaying.DOI: http://dx.doi.org/10.1103/PhysRevD.89.124021Published 18 June 2014Received 16 February 2014© 2014 American Physical Society

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