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In this article, we study the 1 + 3 dimensional relativistic Euler equationson a pre-specified conformally flat expanding spacetime background with spatialslices that are diffeomorphic to $\mathbb{R}^3.$ We assume that the fluidverifies the equation of state $p = c_s^2 \rho,$ where $0 \leq c_s \leq\sqrt{1/3}$ is the speed of sound. We also assume that the inverse of the scalefactor associated to the expanding spacetime metric verifies a $c_s-$dependenttime-integrability condition. Under these assumptions, we use the vectorfieldenergy method to prove that an explicit family of physically motivated,spatially homogeneous, and spatially isotropic fluid solutions is globallyfuture-stable under small perturbations of their initial conditions. Theexplicit solutions corresponding to each scale factor are analogs of thewell-known spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker family. Ournonlinear analysis, which exploits dissipative terms generated by theexpansion, shows that the perturbed solutions exist for all future times andremain close to the explicit solutions. This work is an extension of previousresults, which showed that an analogous stability result holds when thespacetime is exponentially expanding. In the case of the radiation equation ofstate $p = (1/3)\rho,$ we also show that if the time-integrability conditionfor the inverse of the scale factor fails to hold, then the explicit fluidsolutions are unstable. More precisely, we show that arbitrarily small smoothperturbations of the explicit solutions' initial conditions can launchperturbed solutions that form shocks in finite time. The shock formation proofis based on the conformal invariance of the relativistic Euler equations when$c_s^2 = 1/3,$ which allows for a reduction to a well-known result ofChristodoulou.

The Stabilizing Effect of Spacetime Expansion on Relativistic Fluids With Sharp Results for the Radiation Equation of State