Stabilizing Relativistic Fluids on Spacetimes with Non-Accelerated Expansion

Abstract

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