  We study the stability of the isotropic vacuum Friedmann universe in gravity
theories with higher-order curvature terms of the form $(R_{ab}R^{ab})^{n}$
added to the Einstein-Hilbert Lagrangian of general relativity on approach to
an initial cosmological singularity. Earlier, we had shown that, when $% n=1$,
a special isotropic vacuum solution exists which behaves like the
radiation-dominated Friedmann universe and is stable to anisotropic and small
inhomogeneous perturbations of scalar, vector and tensor type. This is
completely different to the situation that holds in general relativity, where
an isotropic initial cosmological singularity is unstable in vacuum and under a
wide range of non-vacuum conditions. We show that when $n\neq 1$, although a
special isotropic vacuum solution found by Clifton and Barrow always exists, it
is no longer stable when the initial singularity is approached. We find the
particular stability conditions under the influence of tensor, vector, and
scalar perturbations for general $n$ for both solution branches. On approach to
the initial singularity, the isotropic vacuum solution with scale factor
$a(t)=t^{P_{-}/3}$ is found to be stable to tensor perturbations for $0.5<n<
1.1309$ and stable to vector perturbations for $0.861425 < n \leq 1$, but is
unstable as $t \to 0$ otherwise. The solution with scale factor
$a(t)=t^{P_{+}/3}$ is not relevant to the case of an initial singularity for
$n>1$ and is unstable as $t \to 0$ for all $n$ for each type of perturbation.
