This paper reports numerical evidence that the standard matter-dominated cosmological model known as the Einstein–de Sitter (EdS) spacetime can be stable when the matter has a tiny nonzero pressure. In earlier work, the same spacetime filled with dust (matter with zero pressure) is known to be dynamically unstable: small inhomogeneities grow and drive the solution away from the homogeneous EdS form. The new results show that adding a small pressure of a particular type can instead smooth out perturbations and drive the system back toward EdS behaviour.

The authors solve the coupled Einstein–Euler equations (Einstein’s equations of general relativity together with fluid dynamics) for a polytropic fluid. A polytropic fluid is described by an equation of state p = K ρ^{1+1/n}, where p is pressure, ρ is density, K>0 is a constant and n is the polytropic index. They restrict the study to Gowdy symmetry, which reduces the problem to one spatial dimension and makes the large-scale numerical experiment feasible. Their code uses a finite-volume method with standard shock-capturing techniques and runs many simulations of small but generic initial perturbations of the homogeneous Friedmann–Lemaître–Robertson–Walker (FLRW) solution that approaches EdS for late times.

At a high level the stabilization comes from pressure coupling density and velocity. Even when the pressure decays as the universe expands, that nonzero pressure lets the fluid homogenize: density and velocity irregularities smooth out instead of steepening into shocks. In the simulations the matter variables decay toward their FLRW values and curvature measures such as the Kretschmann scalar drop, indicating that the spatial geometry becomes flatter and more homogeneous. The authors report that for sufficiently small perturbations and for polytropic indices above a critical value n* the solutions relax toward the EdS asymptotic state.