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PreprintCC BY 4.0arXiv

Lattice Monte Carlo of λϕ4 on Euclidean de Sitter

  • Angelo Caravano
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Abstract

We report the first Monte Carlo simulation of quantum field theory on Euclidean de Sitter space, S4. Rather than discretizing space, we use a spectral lattice based on spherical harmonics, keeping all symmetries exact at finite cutoff. For a massless λϕ4 theory, the zero-mode distribution reproduces the Starobinsky-Yokoyama equilibrium at weak coupling, and deviations closely follow the one-loop renormalization of λ. At strong bare coupling, the renormalized quartic coupling saturates near the ceiling of the one-loop renormalization-group flow. This saturation is the de Sitter counterpart of the triviality mechanism that bounds the Higgs mass in flat space. Our results confirm nonperturbatively that the infrared divergences of light scalars in de Sitter are correctly resummed by the stochastic formalism. More broadly, this work opens up de Sitter space to lattice Monte Carlo methods.

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Cite

BibTeXRIS
BibTeX
@misc{caravano2026lattice,
  title = {{Lattice Monte Carlo of $λϕ^4$ on Euclidean de Sitter}},
  author = {Angelo Caravano},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12547},
  eprint = {2610.12547},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12547},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Lattice Monte Carlo of λϕ^4 on Euclidean de Sitter
AU  - Angelo Caravano
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12547
UR  - https://arxiv.org/abs/2610.12547
AB  - We report the first Monte Carlo simulation of quantum field theory on Euclidean de Sitter space, S^4. Rather than discretizing space, we use a spectral lattice based on spherical harmonics, keeping all symmetries exact at finite cutoff. For a massless λϕ^4 theory, the zero-mode distribution reproduces the Starobinsky-Yokoyama equilibrium at weak coupling, and deviations closely follow the one-loop renormalization of λ. At strong bare coupling, the renormalized quartic coupling saturates near the ceiling of the one-loop renormalization-group flow. This saturation is the de Sitter counterpart of the triviality mechanism that bounds the Higgs mass in flat space. Our results confirm nonperturbatively that the infrared divergences of light scalars in de Sitter are correctly resummed by the stochastic formalism. More broadly, this work opens up de Sitter space to lattice Monte Carlo methods.
ER  -