  We consider cosmological solutions to general relativity with a single
barotropic fluid, where the pressure is a general function of the density, $p =
f(\rho)$. We derive conditions for static and oscillating solutions and provide
examples, extending earlier work to these simpler and more general single-fluid
cosmologies. Generically we expect such solutions to suffer from instabilities,
through effects such as quantum fluctuations or tunneling to zero size. We also
find a classical instability ("no-go" theorem) for oscillating solutions of a
single barotropic perfect fluid due to a necessarily negative squared sound
speed.
