Renormalization of the 2PI Hartree-Fock approximation on de Sitter background in the broken phase

Abstract

The infrared effects for light minimally coupled scalar fields with quartic self-interaction in de Sitter space is investigated using the 2PI effective action formalism. This formalism partially resums infinite series of loop diagrams, and enables us to circumvent the IR divergence problem for a massless minimally coupled scalar field in de Sitter space. It is anticipated that nonperturbative infrared effects generate a curvature-induced mass and self-regulate the IR divergence. However, due to its nonperturbative nature, the renormalization prescription is a nontrivial task. To calculate physical quantities, an appropriate renormalization prescription is required. In this paper, we will show that the MS-like scheme is possible at the Hartree-Fock truncation of the 2PI effective action, and infinite series of divergent terms are needed as counterterms. The phase structure and the quantum backreaction to Einstein's field equation are calculated.

arXiv comment25 pages, 2 figures, title changed, section 1 and 6 revised, typos corrected, results not changed

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• Renormalization group flow and symmetry restoration in de Sitter space
• The Hartree approximation in curved spacetimes revisited I: the effective potential in de Sitter
• Physical momentum representation of scalar field correlators in de Sitter space
• Non-equilibrium dynamics of a scalar field with quantum backreaction
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• Tachyonic production of dark relics: a non-perturbative quantum study
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• Hartree approximation in curved spacetimes revisited II: The semiclassical Einstein equations and de Sitter self-consistent solutions
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