We follow an old suggestion made by Stueckelberg that there exists an intimate connection between weak interaction and gravity, symbolized by the relationship between the Fermi and Newton’s constants. We analyze the hypothesis that the effect of matter upon the metric that represents gravitational interaction in general relativity is an effective one. This leads us to consider gravitation to be the result of the interaction of two neutral spinorial fields ([Formula: see text]-neutrinos) [Formula: see text] and [Formula: see text] with all kinds of matter and energy. We present three examples with only one [Formula: see text]-neutrino: two static and spherically symmetric configurations and a cosmological framework for an isotropic dynamical universe. Without self-interaction, the associated effective geometry is precisely the Schwarzschild metric. On the other hand, a self-interacting [Formula: see text]-neutrino generates a new gravitational black hole.

We analyze the gravitational waves within the Spinor Theory of Gravity (STG) and compare it with the General Relativity proposal. In the case of STG, a gravitational wave may occur if the effective gravitational metric induced by the spinorial field is Ricci flat.

We show that the combined minimal and non minimal interaction with the gravitational field may produce the generation of a cosmological constant without self-interaction of the scalar field. In the same vein we analyze the existence of states of a scalar field that by a combined interaction of minimal and non minimal coupling with the gravitational field can exhibit an unexpected property, to wit, they are acted on by the gravitational field but do not generate gravitational field. In other words, states that seems to violate the action-reaction principle. We present explicit examples of this situation in the framework of a spatially isotropic and homogeneous universe.

We analyze the recently obtained static and spherically symmetric solutions of the Spinor Theory of Gravity (STG) which, in the weak field limit, presents an effective Newtonian potential that contains an extra logarithmic behavior. We apply this solution to the description of the galaxy rotation curves finding an interesting analogy with the dark matter halo profile proposed by Navarro, Frenk and White.