Extension of the Dominant Energy Condition theorem to torsional theories

Determine whether the theorem discussed in the cited reference on the Dominant Energy Condition and causal signal propagation can be usefully extended to the torsional case.

Background

The paper uses the ratio of the spin-density and energy-density length scales to compare the maximum torsion-induced energy flux with the inflaton energy density. Values below unity violate the Dominant Energy Condition, which is presented as a standard means of enforcing causality, although non-minimally coupled scalar fields can violate that condition without necessarily permitting superluminal signal propagation. The applicability of the cited causal theorem to Einstein–Cartan or other torsional settings is left unresolved.

References

Admittedly, it has long been known that (non-minimally coupled) scalar fields, such as the inflaton, can violate this condition (in a certain specific sense) without causing signal propagation outside the light cone; furthermore, it is not clear whether the theorem discussed in can be usefully extended to the torsional case.

How Inflation Might Explain Large-Scale Anisotropy  (2608.19765 - McInnes, 20 Aug 2026) in Section 4, paragraph following equation (BETH)