Gravitational-Wave Propagation in Quadratic Einstein--Cartan--Dirac Gravity: A Conditional Tensor-Sector Analysis
Abstract
We study leading tensor propagation in a specified first-order Einstein--Cartan--Dirac theory with the parity-even quadratic torsion invariant ζTλμνTλμν. Eliminating the nondynamical Lorentz connection on the regular algebraic branch gives a metric description containing the Einstein--Hilbert term, the Dirac action, and a ζ-dependent axial--axial fermion contact interaction. We evaluate the transverse-traceless (TT) Hessian under an explicit factorized mean-field closure, with vanishing connected-current TT response, vanishing first- and second-order TT response of the factorized current scalar, and zero intrinsic TT anisotropic stress. Under these imposed conditions, the leading two-derivative tensor action has QT=MPl2 and cT=1, with no leading dispersion or propagation-induced polarization splitting. These conditions do not follow from isotropy of the one-point axial current, and the present calculation does not derive them from a microscopic fermionic state. The result is therefore conditional and does not establish a general Einstein--Cartan--Dirac no-go theorem. We identify the connected-current TT response that must be calculated to extend the result beyond this closure. Published NANOGrav summaries are used only to check consistency with the GR-like prediction; no new timing-data likelihood or constraint on ζ is obtained.
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BibTeX
@misc{gao2026gravitationalwave,
title = {{Gravitational-Wave Propagation in Quadratic Einstein--Cartan--Dirac Gravity: A Conditional Tensor-Sector Analysis}},
author = {Zhi-Fu Gao and Biao-Peng Li and Na Wang and Hui Wang and Guo-Qiang Jin and Zhoujian Cao and Luiz C. Garcia de Andrade},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07263},
eprint = {2610.07263},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07263},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Gravitational-Wave Propagation in Quadratic Einstein--Cartan--Dirac Gravity: A Conditional Tensor-Sector Analysis
AU - Zhi-Fu Gao
AU - Biao-Peng Li
AU - Na Wang
AU - Hui Wang
AU - Guo-Qiang Jin
AU - Zhoujian Cao
AU - Luiz C. Garcia de Andrade
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.07263
UR - https://arxiv.org/abs/2610.07263
AB - We study leading tensor propagation in a specified first-order Einstein--Cartan--Dirac theory with the parity-even quadratic torsion invariant ζT_λμνT^λμν. Eliminating the nondynamical Lorentz connection on the regular algebraic branch gives a metric description containing the Einstein--Hilbert term, the Dirac action, and a ζ-dependent axial--axial fermion contact interaction. We evaluate the transverse-traceless (TT) Hessian under an explicit factorized mean-field closure, with vanishing connected-current TT response, vanishing first- and second-order TT response of the factorized current scalar, and zero intrinsic TT anisotropic stress. Under these imposed conditions, the leading two-derivative tensor action has Q_T=M_Pl^2 and c_T=1, with no leading dispersion or propagation-induced polarization splitting. These conditions do not follow from isotropy of the one-point axial current, and the present calculation does not derive them from a microscopic fermionic state. The result is therefore conditional and does not establish a general Einstein--Cartan--Dirac no-go theorem. We identify the connected-current TT response that must be calculated to extend the result beyond this closure. Published NANOGrav summaries are used only to check consistency with the GR-like prediction; no new timing-data likelihood or constraint on ζ is obtained.
ER -