Cosmological models in Weyl geometrical scalar-tensor theory

We investigate cosmological models in a recently proposed geometrical theory of gravity, in which the scalar field appears as part of the spacetime geometry. We extend the previous theory to include a scalar potential in the action. We solve the vacuum field equations for different choices of the scalar potential and give a detailed analysis of the solutions. We show that, in some cases, a cosmological scenario is found that seems to suggest the appearance of a geometric phase transition. We build a toy model, in which the accelerated expansion of the early Universe is driven by pure geometry.