Dynamics of Einstein-Aether scalar field cosmology

We study the cosmological evolution of the field equations in the context of Einstein-Aether cosmology by including a scalar field in a spatially flat Friedmann-Lemaitre-Robertson-Walker spacetime. Our analysis is separated into two separate where a pressureless fluid source is included or absent. In particular, we determine the critical points of the field equations and we study the stability of the specific solutions. The limit of general relativity is fully recovered, while the dynamical system admits de Sitter solutions which can describe the past inflationary era and the future late-time attractor. Results for generic scalar field potentials are presented while some numerical behaviours are given for specific potential forms.