Gravitational Waves and Matter Constraints in Gravity from Entropy

Abstract: We show that Gravity from Entropy (GfE) exhibits a tensor-propagation pathology on generic FLRW backgrounds. In vacuum, in the symmetry-inheriting single-multiplet sector, and for the algebraic perfect-fluid constitutive embedding, the strict-principal TT system has a nonzero real characteristic only when (\dot H=K/a^2). Away from this locus the temporal principal roots become complex, signaling a high-frequency hyperbolicity obstruction. Under the stated isotropy assumptions, a rank theorem further shows that one foundational multiplet cannot provide the isotropic bivector response needed to remove this problem.