On the role of the far fields and of cosmology for the theory of gravitation and for the dark matter problem

We give an estimate of the gravitational field of force exerted on a test particle by the far galaxies, in the frame of the weak field approximation. In virtue of Hubble’s law, the action of the far matter turns out to be non negligible, and even the dominant one. An extremely simplified cosmological model is considered. A nonvanishing contribution is obtained only if the discrete and fractal nature of the matter distribution is taken into account. The force per unit mass acting on a test particle is found to be of the order of $0.2c{H}_0$, where $c$ is the speed of light and $H_0$ the present value of Hubble’s constant.