This paper examines the gravitational stability against small perturbations of the quasi-steady state cosmological model. This model was first introduced by Hoyle et al., who in subsequent papers looked at its various theoretical and observational implications. Here we carry out a perturbation analysis of the exact solution of the field equations obtained by Sachs et al. in the noncreative mode which describes the oscillatory feature of this model. We show that the perturbations grow only to a limited amount and then fall off, thus confirming the stability of the solution. We discuss the implications of this result for structure formation in this cosmology.
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