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.
The Hartree approximation in curved spacetimes revisited I: the effective potential in de Sitter
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abstract
We consider a quantum scalar field with {\lambda}{\phi}^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.
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Explicit one-loop computation shows the constraint effective potential for scalars in de Sitter is free of infrared problems and supports its use in stochastic Starobinsky-Yokoyama inflation.
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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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Scalar field effective potentials in de Sitter spacetime
Explicit one-loop computation shows the constraint effective potential for scalars in de Sitter is free of infrared problems and supports its use in stochastic Starobinsky-Yokoyama inflation.