  The linear stability of warped product Einstein metrics as fixed points of
the Ricci flow is investigated. We generalise the results of Gibbons, Hartnoll
and Pope and show that in sufficiently low dimensions, all warped product
Einstein metrics are unstable. By exploiting the relationship between warped
product Einstein metrics, quasi-Einstein metrics and Ricci solitons, we
introduce a new destabilising perturbation (the Ricci variation) and show that
certain infinite families of warped product Einstein metrics will be unstable
in high dimensions.
