Algebraic classification of single-field inflationary dynamics

Abstract

We develop an algebraic classification of canonical single-field inflationary dynamics using an exact depressed cubic equation for the inflaton velocity. Its root structure identifies a branch-swap boundary distinct from the limiting boundary of downhill motion, where ultra-slow-roll inflation naturally emerges. Independently, the conservation of momentum conjugate to the comoving curvature perturbation in the long-wavelength limit provides a criterion for the growth or decay of the gauge-invariant difference between comoving and uniform-density curvature perturbations. Combining these criteria, we construct a unified dynamical chart in terms of the Hubble and potential slow-roll parameters, illustrating its applicability to constant-roll inflation and simple toy models. Our classification shifts the emphasis from assigning models to fixed categories toward understanding the dynamical regimes traversed by inflationary trajectories and their implications for primordial perturbations.

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BibTeX RIS

BibTeX

@misc{gong2026algebraic,
  title = {{Algebraic classification of single-field inflationary dynamics}},
  author = {Jinn-Ouk Gong and Wei-Chen Lin},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07331},
  eprint = {2611.07331},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07331},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Algebraic classification of single-field inflationary dynamics
AU  - Jinn-Ouk Gong
AU  - Wei-Chen Lin
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.07331
UR  - https://arxiv.org/abs/2611.07331
AB  - We develop an algebraic classification of canonical single-field inflationary dynamics using an exact depressed cubic equation for the inflaton velocity. Its root structure identifies a branch-swap boundary distinct from the limiting boundary of downhill motion, where ultra-slow-roll inflation naturally emerges. Independently, the conservation of momentum conjugate to the comoving curvature perturbation in the long-wavelength limit provides a criterion for the growth or decay of the gauge-invariant difference between comoving and uniform-density curvature perturbations. Combining these criteria, we construct a unified dynamical chart in terms of the Hubble and potential slow-roll parameters, illustrating its applicability to constant-roll inflation and simple toy models. Our classification shifts the emphasis from assigning models to fixed categories toward understanding the dynamical regimes traversed by inflationary trajectories and their implications for primordial perturbations.
ER  -

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