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PreprintCC BY 4.0arXiv

Soliton like solutions of λϕ4 theory in de Sitter space

  • D. V. Diakonov
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Abstract

We study classical solutions of a scalar field with quartic potential in de Sitter space-time. Using the ansatz ϕ=F(X·ξ), via embeding coordinate Xα of the ambiend space we find several families of analytic solutions classified by the causal character of the constant vector ξ. For time-like ξ, the solutions are globally regular and describe either global oscillations around a minimum or global vacuum transition; for space-like ξ, they are singular in the global patch but regular in the open slicing. In the Poincaré patch they correspond to contracting bubbles. We compute the classical actions of these solition which are finite only in spacetime dimensions D ≤ 5. We show that the D=4 global vacuum transition solution has the radiation equation of state w=1/3. In D=4 global vacuum transition solution, the retarded Green's function acquires a growing tail as compared to the Green's function on top of vacuum, implying that the transition amplifies the signal at late times.

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Cite

BibTeXRIS
BibTeX
@misc{diakonov2026soliton,
  title = {{Soliton like solutions of $λϕ^4$ theory in de Sitter space}},
  author = {D. V. Diakonov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39459},
  eprint = {2609.39459},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39459},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Soliton like solutions of λϕ^4 theory in de Sitter space
AU  - D. V. Diakonov
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39459
UR  - https://arxiv.org/abs/2609.39459
AB  - We study classical solutions of a scalar field with quartic potential in de Sitter space-time. Using the ansatz ϕ=F(X·ξ), via embeding coordinate X_α of the ambiend space we find several families of analytic solutions classified by the causal character of the constant vector ξ. For time-like ξ, the solutions are globally regular and describe either global oscillations around a minimum or global vacuum transition; for space-like ξ, they are singular in the global patch but regular in the open slicing. In the Poincaré patch they correspond to contracting bubbles. We compute the classical actions of these solition which are finite only in spacetime dimensions D ≤ 5. We show that the D=4 global vacuum transition solution has the radiation equation of state w=1/3. In D=4 global vacuum transition solution, the retarded Green's function acquires a growing tail as compared to the Green's function on top of vacuum, implying that the transition amplifies the signal at late times.
ER  -