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arXiv · 2609.01047

Ultraviolet Closure in Asymptotically Weyl-Invariant Gravity

Daniel Coumbe
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Abstract

We investigate asymptotically Weyl-invariant gravity (AWIG) in the Palatini formulation, defined by an exponent n that interpolates between an Einstein-like infrared regime, where n goes to one, and a Weyl-invariant ultraviolet regime, where n goes to two. In four dimensions, we show that exact Weyl invariance within the minimal scalar Palatini f(R) sector uniquely selects the R^2 action as the ultraviolet endpoint. Interpreting the exponent as an effective curvature-dependent quantity, we constrain a phenomenological class of smooth autonomous flows compatible with the required infrared and ultraviolet endpoints. We then analyse the strict ultraviolet theory. On the regular branch R not equal to zero, and within a restricted torsionless, parity-even sector constructed purely from curvature, all admissible divergent on-shell counterterms reduce at arbitrary loop order to the original \sqrt{-g}R^2 term plus a topological Euler density. Although this conditional result does not establish full off-shell perturbative renormalizability, it provides nontrivial evidence for improved ultraviolet behaviour relative to Einstein gravity and identifies a concrete target for a future first-principles renormalization-group calculation.

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Daniel Coumbe. 2026-09-01. Ultraviolet Closure in Asymptotically Weyl-Invariant Gravity. https://arxiv.org/abs/2609.01047

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