Linearised Dynamics and Physical Degrees of Freedom in Dynamical Torsion Gravity

Dynamical torsion theories provide a geometric extension of general relativity in which additionalspacetime degrees of freedom may propagate. For any such theory to be physically viable, itmust satisfy a minimal “certification” criterion:• the linearised initial value problem is well posed,• all propagating modes are identified and canonically normalised,• ghost and gradient instabilities are absent on physically relevant backgrounds,• and the physical Hilbert space is clearly defined.The purpose of this paper is to provide this certification for the dynamical torsion model underlying the Expansion–Compaction–Torsion (ECT) framework. Our focus is deliberatelyrestricted to the linear regime, where rigorous field-theoretic control is possible and observationalconstraints are applied. The torsion sector studied here is motivated by the ECT geometricframework, in which torsion emerges as an independent dynamical field .