Holographic cosmological backgrounds, Wilson loop (de)confinement and dilaton singularities

We review a construction of holographic geometries dual to ℳ︁ = 4 SYM theory on a Friedmann‐Robertson‐Walker background and in the presence or absence of a gluon condensate and instanton density. We find the most general solution with arbitrary scale factor and show that it is diffeomorphic to topological black holes. We introduce a time‐dependent boundary cosmological constant λ(t) and show energy‐momentum conservation in this background. For constant λ, the deconfinement properties of the temporal Wilson loop are analysed. In most cases the Wilson loop confines throughout cosmological evolution. However, there is an exceptional case which shows a transition from deconfinement at early times to confinement at late times. We classify the presence or absence of horizons, with important implications for the Wilson loop.