Anti-Ultralocality and Plateau Models of Inflation
Abstract
Anti-ultralocality refers to the growth of spatial gradient terms relative to velocity terms in the coupled Einstein--scalar field equations. It is a characteristic feature of decelerated expansion before the onset of inflation. Previous numerical relativity studies have shown that anti-ultralocality prevents the onset of inflation in models with power-law inflaton potentials. In this paper, we show that models with plateau-shaped inflaton potentials, which are considered to be the simplest way to generate a tensor-to-scalar ratio below current observational upper limits, are especially vulnerable to anti-ultralocality effects. The reasons are the flatness of the plateau and the energy density gap of ∼ 10 orders of magnitude between the Planck density and the plateau potential energy. To study the problem, we develop a protocol for assessing the viability of inflationary models in general, and we apply it to a plateau potential using a previously validated numerical relativity code. We find that, starting from generic initial conditions, the growth of gradient terms in the Einstein equations relative to non-gradient terms either prevents inflation from lasting for enough e-folds or triggers a phase of quantum runaway. We show that the fine-tuning of initial conditions necessary to avoid these issues becomes more severe as the energy scale of inflation is made smaller, disfavoring common approaches for reducing the tensor-to-scalar ratio.
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BibTeX
@misc{shterenberg2026antiultralocality,
title = {{Anti-Ultralocality and Plateau Models of Inflation}},
author = {Joshua Shterenberg and David Garfinkle and Anna I. Rosenzweig and David Shlivko and Paul J. Steinhardt},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.24997},
eprint = {2608.24997},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.24997},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Anti-Ultralocality and Plateau Models of Inflation
AU - Joshua Shterenberg
AU - David Garfinkle
AU - Anna I. Rosenzweig
AU - David Shlivko
AU - Paul J. Steinhardt
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2608.24997
UR - https://arxiv.org/abs/2608.24997
AB - Anti-ultralocality refers to the growth of spatial gradient terms relative to velocity terms in the coupled Einstein--scalar field equations. It is a characteristic feature of decelerated expansion before the onset of inflation. Previous numerical relativity studies have shown that anti-ultralocality prevents the onset of inflation in models with power-law inflaton potentials. In this paper, we show that models with plateau-shaped inflaton potentials, which are considered to be the simplest way to generate a tensor-to-scalar ratio below current observational upper limits, are especially vulnerable to anti-ultralocality effects. The reasons are the flatness of the plateau and the energy density gap of ∼ 10 orders of magnitude between the Planck density and the plateau potential energy. To study the problem, we develop a protocol for assessing the viability of inflationary models in general, and we apply it to a plateau potential using a previously validated numerical relativity code. We find that, starting from generic initial conditions, the growth of gradient terms in the Einstein equations relative to non-gradient terms either prevents inflation from lasting for enough e-folds or triggers a phase of quantum runaway. We show that the fine-tuning of initial conditions necessary to avoid these issues becomes more severe as the energy scale of inflation is made smaller, disfavoring common approaches for reducing the tensor-to-scalar ratio.
ER -