Projective invariance in cosmological models and dark energy

We study theories of gravitation that are based on the Einstein - Hilbert action that are not projectively invariant and can therefore completely determine their connections. We are thus lead to the conclusion that the geometry is necessarily Riemann - Cartan and at least the trace part of a torsion field must be present. We examine the consequence of including these torsion fields in cosmological models. Our results differ from those obtained earlier in the Einstein - Cartan - Sciama - Kibble theory. We also consider a model that includes a series of quadratic torsion terms. This series leads to a potential function that has the effect of "turning on" the cosmological constant. This potential function then acts like dark energy. This model also shows that the torsion field can produce an inflationary period.