What question did this study set out to answer?

The aim is to present a unique theory branch in Defect Cartan Gravity that limits additional degrees of freedom.

March 13, 2026Open Access

Defect Cartan Gravity I: Emergent Coframes and the Minimal Spin-0+ Torsion Sector

Key Points

The aim is to present a unique theory branch in Defect Cartan Gravity that limits additional degrees of freedom.
Utilized Cartan variables (coframe and Lorentz connection) in the analysis.
Imposed a parity-even quadratic restriction to resolve potential issues with ghost states.
Conducted variational structure analysis and derived field equations in covariant form.
Explored the relationship between torsion and scalar curvature through trace-only reduction.
Linearized equations around Minkowski space to identify propagating degrees of freedom.
Presented concrete health conditions ensuring the absence of ghosts and tachyons.
Showed how additional scalar degrees of freedom could be maintained without introducing instability.
Derived field equations that are robust under controlled decoupling limits.

Abstract

This paper fixes the unique theory branch used by Defect Cartan Gravity. We workin Cartan variables (coframe and Lorentz connection) and impose a parity-even quadraticrestriction engineered to propagate only one additional scalar (spin-0+) connection/torsiondegree of freedom beyond General Relativity in the macroscopic spinless regime. Therestriction avoids the generic spin-2 ghost that accompanies broad curvature-squared sectors.We present: (i) the action and parameter dictionary; (ii) torsion irreducible decompositionand the meaning of the 0+ branch; (iii) full variational structure and field equations incovariant form and in a useful component reduction; (iv) an auxiliary-field (scalar-tensor)rewriting of the R2 sector; (v) the trace-only torsion reduction, showing how the tracetorsion mixes with the scalar curvature sector and how the remaining torsion irreps arenondynamical for spinless sources; (vi) linearization around Minkowski space and isolationof the propagating content; and (vii) concrete health conditions (no ghosts/tachyons) andcontrolled decoupling limits. Papers II and III treat this paper as the definitive theory lockand do not introduce new gravitational degrees of freedom.

Defect Cartan Gravity I: Emergent Coframes and the Minimal Spin-0+ Torsion Sector

Key Points

Abstract

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