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Scalar effective potentials in de Sitter spacetime

Lucas Vicente García-Consuegra*

Arttu Rajantie†

  • Theoretical Physics Department, CERN, 1211 Geneva 23, Switzerland and Abdus Salam Centre for Theoretical Physics, Imperial College London, London, SW7 2AZ, United Kingdom

  • *Contact author: lucas.vicente_garcia-consuegra@kcl.ac.uk
  • †Contact author: a.rajantie@imperial.ac.uk
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Phys. Rev. D 113, 125016 – Published 12 June, 2026

DOI: https://doi.org/10.1103/tkw7-dkq6

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 spacetime. 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 to 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.

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Phys. Rev. D 113, 125016– Published 12 June, 2026
  • Received 10 February 2026
  • Accepted 13 May 2026
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