Hartree approximation in curved spacetimes revisited II: The semiclassical Einstein equations and de Sitter self-consistent solutions

Abstract

We consider the semiclassical Einstein equations (SEE) in the presence of a quantum scalar field with self-interaction $\lambda {\varphi }^4$. Working in the Hartree truncation of the two-particle irreducible (2PI) effective action, we compute the vacuum expectation value of the energy-momentum tensor of the scalar field, which act as a source of the SEE. We obtain the renormalized SEE by implementing a consistent renormalization procedure. We apply our results to find self-consistent de Sitter solutions to the SEE in situations with or without spontaneous breaking of the $Z_2$-symmetry.

32 pages, 4 figures

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Cited by in corpus (5)

• Scalar field correlator in de Sitter space at next-to-leading order in a 1/N expansion
• Quantum scalar fields in de Sitter space from the nonperturbative renormalization group
• Nonperturbative renormalization group for scalar fields in de Sitter space: beyond the local potential approximation
• To the sphere and back again: de Sitter infrared correlators at NTLO in 1/N
• Quantum backreaction of $O(N)$-symmetric scalar fields and de Sitter spacetimes at the renormalization point: renormalization schemes and the screening of the cosmological constant