Stabilizing Relativistic Fluids on Spacetimes with Non-Accelerated Expansion

We establish global regularity and stability for the irrotational relativistic Euler equations with equation of state $$\bar{p}{}=K\bar{\rho }{}$$ , where $$0<K<1/3$$ small initial data in expanding direction FLRW spacetimes form $$(\mathbb R\times \mathbb T^3,-d\bar{t}{}^2+\bar{t}{}^2\delta _{ij} dx^i dx^j$$ ). This provides first case non-dust fluid stabilization by spacetime expansion rate is power law type but non-accelerated. In particular, time integral inverse scale factor diverges as $$t\rightarrow \infty $$ . The result implies that structure formation cosmological evolution associated development shocks fluids necessarily requires a phase deccelerating Universe to occur matter massive.