The Hartree approximation in curved spacetimes revisited I: the effective potential in de Sitter

Abstract

We consider a quantum scalar field with λϕ^4 interaction in curved spacetimes. The quantum effects are taken into account nonperturbatively using the Hartree approximation to the 2PI effective action. Although this approximation has been considered in many previous works, we reconsider it using a consistent nonperturbative renormalization procedure, which we extend to general curved spacetimes. We obtain the renormalized equations for the mean field and for the propagator of the fluctuations, showing explicitly their independence on the arbitrary scale introduced by the regularization scheme. We apply our results to the particular case of de Sitter spacetime and discuss spontaneous symmetry breaking. The results depend strongly on the renormalization procedure.

40 pages, 8 figures

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• Quantum scalar fields in de Sitter space from the nonperturbative renormalization group
• Characters of different secular effects in various patches of de Sitter space
• Infrared dynamics of massive scalars from the complementary series in de Sitter space
• 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
• Light scalars on cosmological backgrounds
• Stochastic inflation from quantum field theory and the parametric dependence of the effective noise amplitude
• Hartree approximation in curved spacetimes revisited II: The semiclassical Einstein equations and de Sitter self-consistent solutions
• 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
• Scalar field effective potentials in de Sitter spacetime