Massive Gravity as an Alternative Gravity
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Massive Gravity as an Alternative Gravity Y. Sobouti* Institute for Advanced Studies in Basic sciences (IASBS) Received July 2, 2019; revised November 25, 2019; accepted December 2, 2019
Abstract—The Newtonian gravity force is massless and decreases as 1/r2 , too steeply to explain the flat rotation curves of spiral galaxies. Massive gravity, on the other hand, drops as 1/r and is capable of doing the job. Massive fields have a respected record in the history of field theories. We follow the suit and add a “mass term” to the field equation of Newtonian gravity, which, to begin with, is static. Next, we use the observation-based Tully-Fisher relation to determine the nature and characteristics of the added mass term. We are able to produce the rotation curves flat enough to justify the observational data up to several optical radii of the galaxies, where observations are both abundant and reliable. At very far distances, however, massive gravity goes through a sequence of intermittently attractive and repulsive phases. This is a welcome novelty. It may enable one to address the wavy fluctuations and patchy voids that are not uncommon in the archives of observed rotation curves. With a stretch of imagination, massive gravity may find an observational support in the Oort clouds, a stipulated spherical shell of debris at farthest outreaches of the Solar system. DOI: 10.1134/S0202289320010132
1. INTRODUCTION
The Tully-Fisher relation, that rotation curves, more often than not, have flat asymptotes, and the asymptotic speeds are more or less proportional to the fourth root of the luminosities (masses) of the spirals, plays a pivotal role in determining the characteristics of the mass of massive gravity. The paper is organized as follows. In Section 2, for pedagogical reasons and in order to see the lineage of what we propose here to what already exists in the literature, we give a brief review of massive gravity waves. In Section 3 we introduce our static massive gravity, extract the mass parameter of the field from the Tully-Fisher relation, and demonstrate that the proposed static massive gravity is indeed capable of giving rotation curves flat enough to explain the bulk of the archived data. In Section 4 we explore possible observational implications of the theory in the Solar system and its possible tests in galactic environments. In Section 5 we summarize our conclusions and list an agenda items for future follow-up.
Zwicky [1] is credited for a decisive inference that the Newtonian gravity of the observable matter in galaxies is much too weak to explain the flat rotation curves of spiral galaxies, or the large velocity dispersions in elliptic galaxies and clusters of galaxies. Since then, vast literature has followed. Attempts to resolve the puzzle range from a variety of alternative theories of gravity to a multitude of dark matter scenarios. What we propose here might be categorized as an alternative theory of gravity. We argue that the Newtonian massless, 1/r 2 , force dies away too steeply to explain the dynamics of gal
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