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Analytic solutions in Einstein-aether scalar field cosmology

In the context of Einstein-aether scalar field cosmology we solve the field equations and determine exact and analytic solutions. In particular, we consider a model proposed by Kanno and Soda where the aether and the scalar fields interact through the aether coefficient parameters, which are promoted to be functions of the scalar field. For this model, we write the field equations by using the minisuperspace approach and we determine the scalar field potentials which leads to Liouville--integrable systems. We solve the field equations for five families of scalar field potentials and, whether it is feasible, we write down the analytic solutions by using closed-form functions.