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Modified Newtonian Dynamics (MoND) is an empirically modification ofNewtonian gravity at largest scales in order to explain rotation curves ofgalaxies, as an alternative to nonbaryonic dark matter. But MoND theories canhardly connect themselves to the formalism of relativistic cosmology typeFriedmann-Robertson-Walker. The present work posits the possibility of buildingthis connection by postulating a Yukawa-like scalar potential, with nongravitational origin. This potential comes from a simple reflection speculateof the well-know potential of Yukawa and it is intended to describe thefollowing physics scenarios: null in very near solar system, slightlyattractive in ranges of interstellar distances, very attractive in distanceranges comparable to galaxies cluster, and repulsive to cosmic scales. As aresult of introducing this potential into the typical Friedman equations wefound that the critical density of matter is consistent with the observeddensity (without a dark matter assumption), besides this, MoND theory isobtained for interstellar scales and consequently would explain rotationcurves. Also it is shown that Yukawa type inverse does not alter thepredictions of the Cosmic Microwave Background neither the primordialnucleosinthesys in early universe; and can be useful to explain the large-scalestructure formation.

Theory MOND in a Friedmann-Robertson-Walker Cosmology as alternative to the Nonbaryonic Dark Matter paradigm