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 p¯ = Kρ¯ , where 0 < K< 1 / 3 , for small initial data in the expanding direction of FLRW spacetimes of the form (R× T3, - dt¯ 2+ t¯ 2δijdxidxj). 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→ ∞. 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.