  We investigate cosmological models in a recently proposed geometrical theory
of gravity, in which the scalar field appears as part of the space-time
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.
