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  • Open Access

Pathologies of dimension-zero scalar fields

James M. Cline*

Anamaria Hell†

  • McGill University Department of Physics and Trottier Space Institute, 3600 Rue University, Montreal, Quebec H3A 2T8, Canada

  • *Contact author: jcline@physics.mcgill.ca
  • †Contact author: anamaria.hell@ipmu.jp
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Phys. Rev. D 114, 045022 – Published 24 August, 2026

DOI: https://doi.org/10.1103/63ck-c9rh

Abstract

It has been claimed in a series of papers that scalar fields with a fourth-order Lagrangian∼(□φ)2 can solve the cosmological constant problem by canceling the loop contributions from standard model fields, and that their fluctuations can be the source of the primordial density perturbations of the Universe, without the need for inflation. We dispute these claims. The spectrum of the theory includes a ghost, which leads to classical instabilities and quantum violation of unitarity. We show that the new scalar particles cannot cancel the standard model contributions to the cosmological constant, unless they include a unitarity-violating ghost at the quantum level. Further, the coupling of such scalars to the particles of the standard model induces a confining fifth force which rules it out as a source of density perturbations in the early Universe.

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Phys. Rev. D 114, 045022– Published 24 August, 2026
  • Received 23 March 2026
  • Accepted 14 July 2026
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