Abstract
Gravitational theories outside standard general relativity have been drawing increased attention over the past several years, mostly due to the lack of direct observational evidence of dark matter. With some recent very high level dark matter searches continuing, and the parameter space to search decreasing has lead to a new interest in rethinking gravity at the largest of scales. As an alternative gravitational theory, conformal gravity has enjoyed much of the success of Modified Newtonian Dynamics (MOND) in predicting phenomenology, but differs dramatically in its initial construction. In this work, we explore some recent advances in conformal gravity, which help to build the case for support of such an alternative theory. Here, we highlight conformal gravity’s success in fitting new rotation curves, its ability to explain velocity dispersions in clusters, the initial steps towards gravitational lensing and finally, some preliminary work on explaining universal centripetal acceleration trends in galaxies.
Highlights
Conformal gravity is a fourth order renormalizable metric theory of gravity, where the Ricci scalar in the Einstein-Hilbert action is replaced by the square of the conformal Weyl tensor as: IW = −αg d4x(−g)1/2CλμνκCλμνκ= −2αg d4x(−g)1/2 RμκRμκ − (1/3)(Rαα)[2 ], (1) where + Rαα (2)is the conformal Weyl tensor and the gravitational coupling constant αg is dimensionless
The goal of this paper is to summarize some recent conformal gravity fits to rotation3–6curves, to show how conformal gravity can address the cluster motion problem without invoking dark matter, and develop the initial framework for gravitational lensing formalism in conformal gravity
In this paper we reviewed some recent important advancements in conformal gravity
Summary
Is the conformal Weyl tensor and the gravitational coupling constant αg is dimensionless This action, when varied with respect to the metric (as in standard gravity1), yields the conformal gravity field equations, 4αgW μν = 4αg. These equations were later solved by Mannheim and Kazanas[2] for a spherical mass, exterior solution, which behaves as a conformal gravity Schwarzchild like solution, and allows for application of the theory to various data sets. While the rotation curve fitting provides direct data that can be tested against the predictions of an alternative model of gravity, there are other observational motivations for the existence of dark matter, such as the motion of galaxies in clusters and gravitational lensing. The authors above have made an initial pass at conformal gravity’s answer to this new found phenomena, and we report the preliminary findings in this work
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