  In this article, we study the 1 + 3 dimensional relativistic Euler equations
on a pre-specified conformally flat expanding spacetime background with spatial
slices that are diffeomorphic to $\mathbb{R}^3.$ We assume that the fluid
verifies 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 scale
factor associated to the expanding spacetime metric verifies a $c_s-$dependent
time-integrability condition. Under these assumptions, we use the vectorfield
energy method to prove that an explicit family of physically motivated,
spatially homogeneous, and spatially isotropic fluid solutions is globally
future-stable under small perturbations of their initial conditions. The
explicit solutions corresponding to each scale factor are analogs of the
well-known spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker family. Our
nonlinear analysis, which exploits dissipative terms generated by the
expansion, shows that the perturbed solutions exist for all future times and
remain close to the explicit solutions. This work is an extension of previous
results, which showed that an analogous stability result holds when the
spacetime is exponentially expanding. In the case of the radiation equation of
state $p = (1/3)\rho,$ we also show that if the time-integrability condition
for the inverse of the scale factor fails to hold, then the explicit fluid
solutions are unstable. More precisely, we show that arbitrarily small smooth
perturbations of the explicit solutions' initial conditions can launch
perturbed solutions that form shocks in finite time. The shock formation proof
is 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 of
Christodoulou.
