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 QFT with a quartic self-interaction in de Sitter. 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 non-perturbative 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 non-perturbative sum is decaying.Keywords
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