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Resummation of infrared logarithms in de Sitter space via Dyson-Schwinger equations: the ladder-rainbow approximation
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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.
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Yukawa scalar self energy at two loop and $\langle \phi^2 \rangle$ in the inflationary de Sitter spacetime
Two-loop Yukawa corrections in de Sitter yield ⟨ϕ²⟩ ~ ln⁴a at late times, with a resummed expression that is bounded, decreases with larger Yukawa coupling, and implies a growing dynamical scalar mass.
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