A recent study has explored the implications of the Bianchi identity in multi-fluid, matter-type modified gravity cosmological models. Researchers have shown that, while the Bianchi identity constrains the divergence of the total effective stress tensor, it does not, by itself, determine the currents assigned to its constituent matter sectors. These currents are only selected after the off-shell matter action or an additional phenomenological closure has been specified, highlighting the distinction between action-level predictions and closure artifacts in matter-type gravity.

The work focused on a spatially flat two-fluid background inspired by scale-independent EMSG (Energy-Momentum-Squared Gravity), combining an algebraic perfect-fluid prescription with a vanishing contracted-Hessian contribution. Separate conservation of the total conventional and modification sectors was assumed. For unequal equations of state and every α≠0, this closure yields a Barrow-Clifton system whose transfer coefficients depend on the fluid equations of state (w1, w2) but not on α. This reveals a singularity: the α→0 limit of this family does not recover the uncoupled GR conservation laws.

The authors solved the two density eigenmodes and derived the associated modified Liénard equation for the Hubble parameter (H). They also proved that the discriminant governing rank loss of the density-reconstruction map is strictly positive for every finite w1≠w2, implying that each genuinely quadratic case has two distinct real rank-degenerate couplings. Exact vacuum and stiff-fluid families were used to illustrate modal cancellation. These results provide a crucial consistency diagnostic for separating genuine action-level predictions from closure artifacts in multi-fluid, matter-type gravity models, although they do not establish an observationally viable EMSG model on their own.