  For $1/3<K<1$, we consider the stability of two distinct families of
spatially homogeneous solutions to the relativistic Euler equations with a
linear equation of state $p=K\rho$ on exponentially expanding FLRW spacetimes.
The two families are distinguished by one being spatially isotropic while the
other is not. We establish the future stability of nonlinear perturbations of
the non-isotropic family for the full range of parameter values $1/3<K<1$,
which improves a previous stability result established by the second author
that required $K$ to lie in the restricted range $(1/3,1/2)$. As a first step
towards understanding the behaviour of nonlinear perturbations of the isotropic
family, we construct numerical solutions to the relativistic Euler equations
under a $\mathbb{T}^2$-symmetry assumption. These solutions are generated from
initial data at a fixed time that is chosen to be suitably close to the initial
data of an isotropic solution. Our numerical results reveal that, for the full
parameter range $1/3<K<1$, the density contrast $\frac{\partial_{x}\rho}{\rho}$
associated to a nonlinear perturbation of an isotropic solution develops steep
gradients near a finite number of spatial points where it becomes unbounded at
future timelike infinity. This behaviour, anticipated by Rendall in
\cite{Rendall:2004}, is of particular interest since it is not consistent with
the standard picture for inflation in cosmology.

General Relativity and Quantum Cosmology;Analysis of PDEs