The Effect of Interplay between the Newtonian Gravitational Field and the Cosmological Expansion
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The Effect of Interplay between the Newtonian Gravitational Field and the Cosmological Expansion A. Feoli1* , E. Benedetto1, 2 , and A. L. Iannella1 1
2
Department of Engineering, University of Sannio, Piazza Roma 21, I-82100 Benevento, Italy Department of Informatics, University of Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano, Italy Received January 10, 2020; revised February 20, 2020; accepted February 25, 2020
Abstract—We study the motion of a celestial body under the simultaneous effect of the Newtonian and cosmological fields. The resulting effect is not only interesting by itself, but it could also give a contribution to solving the well-known problem of galactic rotation curves without the assumption of the existence of dark matter. We assume that in the outer regions of galaxies the stars and the hydrogen clouds follow not only the geodesics of the central field, but also the Hubble flow. By a simple application of the classical kinematics of relative motions, we analyze the effects of the composition of these two motions, and we find an increase of the rotation speed with respect to the galactic center that could be the cause of the nonNewtonian behavior of the rotation curves. DOI: 10.1134/S0202289320020061
1. INTRODUCTION It is well known that the evolution of the Universe is commonly described by the so-called ΛCDM model. This model has been developed thanks to the experimental observations of supernovae [1, 2], clustering of galaxies [3–5] and the Cosmic Microwave Background [6–8]. At present, it is believed that the Universe is composed by 68.5% of Dark Energy (DE), 4.9% of ordinary luminous matter and 26.6% of Dark Matter (DM) [9]. While DE was introduced recently after the discovery of the Universe acceleration, DM has a more ancient history. Indeed, it was conceived when Zwicky measured the velocities of the Coma cluster of galaxies [10]. Subsequently, the observations of the galactic rotation curves, thanks above all to Vera Rubin’s research group, have unequivocally demonstrated that they do not have the expected Keplerian behavior GM (1) v= r In fact, at large distances from the center, the speeds are approximately constant, or even weakly increasing. The most surprising behavior concerns above all the regions outside the luminous part of the galaxy, where, for example, neutral hydrogen clouds rotate at a tangential velocity that seems not to decay with distance. Certainly, this behavior can be explained by postulating the existence of a Dark Matter halo, *
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but also other different approaches are in principle possible, at least until dark matter particles are really found. The most popular alternative points of view are related to generalizations of Einstein’s general relativity, but also simpler models were proposed, assuming new properties of space-time itself as vorticity [11] or plasticity [12]. On the other side, the best known attempt to find an explanation of the rotation curves without dark matter is the one developed in 1983 by Milgrom, the so-called MOND (
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