We show that the recently proposed conformally invariant model for the gravitational field, based on fourth-rank geometry, is equivalent, in vacuum, to general relativity with a non-vanishing cosmological constant coupled to a Weyl vector field. Recent observational evidence suggests a non-vanishing cosmological constant and an essential anisotropy in the large-scale structure of the universe, supporting our model. We also couple the model to matter in the low-energy regime where the conformal invariance has been broken.
