Oscillating and Static Universes from a Single Barotropic Fluid

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We consider cosmological solutions to general relativity with a single barotropic fluid, where the pressure is a general function of the density, p = f(ρ). 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.