Unified phantom cosmologies

We present a general algorithm based on the concept of form-invariance which can be used for generating phantom cosmologies. It involves linear transformations between the kinetic energy and the potential of the scalar field, and transforms solutions of the Einstein-Klein-Gordon equations which preserve the weak energy condition into others which violate it, while keeping the energy density of the field positive. All known solutions representing phantom cosmologies are unified by this procedure. Using the general algorithm we obtain those solutions and show the relations between them. In addition, the scale factors of the product and seed solutions are related by a generalization of the well-known $a\to a^{-1}$ duality.