Modification of the Newtonian Dynamics in &#923FRW-Cosmology an Alternative Approach to Dark Matter and Dark Energy

Abstract

Modified Newtonian Dynamics (MoND) is an empirically motivated modification of Newtonian gravity at largest scales, to explain rotation curves of galaxies, as an alternative to nonbaryonic dark matter. But MoND theories can hardly connect to the formalism of relativistic cosmology type Friedmann-Robertson-Walker. Presently work intends the existence of one scalar potential, with non gravitational origin, that would solve these problems. This potential Yukawa type inverse is build starting from a specular reflection of the potential of Yukawa: null in very near solar system, slightly attractiveness in ranges of interstellar distances, very attractiveness in distance ranges comparable to galaxies cluster and repulsive to cosmic scales. The consequences of this potential are discussed, through Cosmological Model Tipe Friedmann-Roberston-Walker with cosmological term in function of the distance (lambda like function of r). In the cosmological model so raised the critical density of matter is consistent with the observed density does not include dark matter, MoND theory is dedu c ed for interstellar scales and consequently would explain rotation curves. Also it is shown that Yukawa type inverse does not alter the predictions of the Cosmic Microwave Background neither the primordial nucleosynthesis in early universe; and can be explain the large-scale structure formation.