Logarithmic gravity from a very slow roll limit of inflation
Abstract
We study the inflationary no-boundary wavefunction in a ``linear-roll limit,'' in which GN → 0 while the Hubble scale H and the slope of the inflaton potential are held fixed. Although bulk graviton fluctuations are suppressed in this limit, quantum inflaton fluctuations remain finite. Because reheating occurs on a surface of fixed inflaton value, these fluctuations become fluctuations of the conformal factor of the reheating metric. The probability measure for these fluctuations simplifies drastically and becomes Gaussian, even for large fluctuations. The resulting log-correlated theory at superhorizon scales is a d-dimensional analog of Liouville gravity without the exponential potential, which we call Logarithmic Gravity. The quadratic and linear terms are determined by conformally covariant scattering data; in even dimensions we relate them to the critical GJMS operator and Branson Q-curvature. From bulk unitarity, we argue that one-loop effects do not generate additional conformal-factor dependence in the physical probability measure, and we verify the cancellation explicitly in 2 + 1 dimensions. For the no-boundary norm with a rolling inflaton, we show that the noncompact residual conformal symmetries can be gauge fixed with a finite Faddeev-Popov determinant, so they do not force the sphere contribution to vanish. In addition, conditioning on the absence of vacuum decay by bubble nucleation generates the Liouville exponential potential in the probability measure.
Related
- Analytic results for slow-roll curved-space inflation and exponential potentials
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- Constant-Roll Inflation as a Competitive Alternative to Slow-Roll Inflation
- Ultra-slow-roll Inflation with Non-perturbative Non-Gaussianity and Scalar Induced Gravitational Waves
BibTeX
@misc{cotler2026logarithmic,
title = {{Logarithmic gravity from a very slow roll limit of inflation}},
author = {Jordan Cotler and Victor Ivo and Juan Maldacena},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38052},
eprint = {2609.38052},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38052},
}
RIS
TY - UNPB
TI - Logarithmic gravity from a very slow roll limit of inflation
AU - Jordan Cotler
AU - Victor Ivo
AU - Juan Maldacena
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38052
UR - https://arxiv.org/abs/2609.38052
AB - We study the inflationary no-boundary wavefunction in a ``linear-roll limit,'' in which G_N → 0 while the Hubble scale H and the slope of the inflaton potential are held fixed. Although bulk graviton fluctuations are suppressed in this limit, quantum inflaton fluctuations remain finite. Because reheating occurs on a surface of fixed inflaton value, these fluctuations become fluctuations of the conformal factor of the reheating metric. The probability measure for these fluctuations simplifies drastically and becomes Gaussian, even for large fluctuations. The resulting log-correlated theory at superhorizon scales is a d-dimensional analog of Liouville gravity without the exponential potential, which we call Logarithmic Gravity. The quadratic and linear terms are determined by conformally covariant scattering data; in even dimensions we relate them to the critical GJMS operator and Branson Q-curvature. From bulk unitarity, we argue that one-loop effects do not generate additional conformal-factor dependence in the physical probability measure, and we verify the cancellation explicitly in 2 + 1 dimensions. For the no-boundary norm with a rolling inflaton, we show that the noncompact residual conformal symmetries can be gauge fixed with a finite Faddeev-Popov determinant, so they do not force the sphere contribution to vanish. In addition, conditioning on the absence of vacuum decay by bubble nucleation generates the Liouville exponential potential in the probability measure.
ER -