Scalar field effective potentials in de Sitter spacetime

Abstract

We investigate two different definitions of a scalar field effective potential in quantum field theory in de Sitter spacetime: the standard textbook definition, and the constraint effective potential proposed by O'Raifeartaigh et al. in 1986. While these definitions are equivalent in Minkowski spacetime, they differ significantly in de Sitter. We demonstrate this by computing them both explicitly at one-loop order in perturbation theory. It is well known that the perturbative expansion of the standard effective potential fails converge for light fields. In contrast, the constraint effective potential does not suffer from this infrared problem, and it can therefore be computed using perturbation theory. We discuss the physical interpretation of the two effective potentials. In particular, we provide evidence supporting an earlier conjecture that the constraint effective potential is the correct one to use in the stochastic Starobinsky-Yokoyama theory.

Minor corrections; accepted in PRD

References in corpus (23)

• Cosmological phase transitions: from perturbative particle physics to gravitational waves
• On Resumming Inflationary Perturbations beyond One-loop
• On the proper treatment of massless fields in Euclidean de Sitter space
• Cosmological Aspects of Higgs Vacuum Metastability
• Effective potential for quantum scalar fields on a de Sitter geometry
• On "dynamical mass" generation in Euclidean de Sitter space
• Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space
• Effective long wavelength scalar dynamics in de Sitter
• Quantum scalar fields in de Sitter space from the nonperturbative renormalization group
• The 1-loop effective potential for the Standard Model in curved spacetime
• BRST quantization of the massless minimally coupled scalar field in de Sitter space (zero modes, euclideanization and quantization)
• Scalar correlation functions in de Sitter space from the stochastic spectral expansion
• On the IR Divergences in de Sitter Space: loops, resummation and the semi-classical wavefunction
• The Hartree approximation in curved spacetimes revisited I: the effective potential in de Sitter
• Resummation of infrared logarithms in de Sitter space via Dyson-Schwinger equations: the ladder-rainbow approximation
• Backreaction of superhorizon scalar field fluctuations on a de Sitter geometry : a renormalisation group perspective
• Nonperturbative infrared effects for light scalar fields in de Sitter space
• Symmetry breaking and the Goldstone theorem in de Sitter space
• Lattice ${\varphi }^4$ Field Theory on Riemann Manifolds: Numerical Tests for the 2-d Ising CFT on ${\mathbb{S}}^2$
• Effective potential and Goldstone bosons in de Sitter space
• Regularizing infrared divergences in de Sitter spacetime: Loops, dimensional regularization, and cutoffs
• Second-order stochastic theory for self-interacting scalar fields in de Sitter spacetime
• Free scalar correlators in de Sitter via the stochastic approach beyond slow roll