Canonical Quantization and Constraint Algebra of Weyl-Invariant Gravity in a Conformal Gauge: Emergence of a Geometric Cosmological Term
Abstract
We present the canonical quantization of Weyl-invariant gravity in a specific conformal gauge. Fixing the scale factor as a(η) = 1/(H0η) yields an effective geometric cosmological term ℳ(η) = α/η2 on the left-hand side of the Einstein equations, guaranteeing an equation of state w = −1 by construction. The Bianchi identity requires a compensator scalar field; we show that this compensator is the conformal mode of the metric, a gauge artifact that does not propagate ghost instabilities in the full quantum theory. We develop the complete ADM Hamiltonian formulation and prove that the constraint algebra closes in standard first-class form. Canonical quantization yields a well-defined Wheeler-DeWitt equation where the ℳ(η) term acts as a potential barrier dynamically suppressing the quantum creation of small-scale universes. The physical reduced Hamiltonian is demonstrated to be bounded from below, time evolution is strictly unitary in the physical Hilbert space, and microcausality is preserved. In the pure vacuum regime, the model admits an exact analytical solution with ΩDE = 1, resolving the cosmic coincidence problem without fine-tuned parameters. In the matter-dominated era, the comoving horizon scales as RH ∝ η, so our result ℳ ∝ η−2 ∝ RH−2 reproduces the central Compton Mass Dark Energy (CMaDE) hypothesis from first principles and establishes n = −2 as the theoretical benchmark for the Conformal Holographic Dark Energy (CHDE) parametrization ℳ ∝ ηn. From a pure conformal symmetry principle, the model delivers an effective geometric cosmological term that drives the accelerated expansion with w = −1, providing the missing action principle for CMaDE.
Versions
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BibTeX
@misc{mezadominguez2026canonical,
title = {{Canonical Quantization and Constraint Algebra of Weyl-Invariant Gravity in a Conformal Gauge: Emergence of a Geometric Cosmological Term}},
author = {Jorge Meza-Domínguez and Tonatiuh Matos},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28542},
eprint = {2609.28542},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28542},
}
RIS
TY - UNPB
TI - Canonical Quantization and Constraint Algebra of Weyl-Invariant Gravity in a Conformal Gauge: Emergence of a Geometric Cosmological Term
AU - Jorge Meza-Domínguez
AU - Tonatiuh Matos
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.28542
UR - https://arxiv.org/abs/2609.28542
AB - We present the canonical quantization of Weyl-invariant gravity in a specific conformal gauge. Fixing the scale factor as a(η) = 1/(H_0η) yields an effective geometric cosmological term ℳ(η) = α/η^2 on the left-hand side of the Einstein equations, guaranteeing an equation of state w = −1 by construction. The Bianchi identity requires a compensator scalar field; we show that this compensator is the conformal mode of the metric, a gauge artifact that does not propagate ghost instabilities in the full quantum theory. We develop the complete ADM Hamiltonian formulation and prove that the constraint algebra closes in standard first-class form. Canonical quantization yields a well-defined Wheeler-DeWitt equation where the ℳ(η) term acts as a potential barrier dynamically suppressing the quantum creation of small-scale universes. The physical reduced Hamiltonian is demonstrated to be bounded from below, time evolution is strictly unitary in the physical Hilbert space, and microcausality is preserved. In the pure vacuum regime, the model admits an exact analytical solution with Ω_DE = 1, resolving the cosmic coincidence problem without fine-tuned parameters. In the matter-dominated era, the comoving horizon scales as R_H ∝ η, so our result ℳ ∝ η^−2 ∝ R_H^−2 reproduces the central Compton Mass Dark Energy (CMaDE) hypothesis from first principles and establishes n = −2 as the theoretical benchmark for the Conformal Holographic Dark Energy (CHDE) parametrization ℳ ∝ η^n. From a pure conformal symmetry principle, the model delivers an effective geometric cosmological term that drives the accelerated expansion with w = −1, providing the missing action principle for CMaDE.
ER -