Flat galactic rotation curves from geometry in Weyl gravity

Abstract

We searched for a resolution of the flat galactic rotation curve problem from geometry instead of assuming the existence of dark matter. We observed that the scale independence of the rotational velocity in the outer region of galaxies could point out to a possible existence of local scale symmetry and therefore the gravitational phenomena inside such regions should be described by the unique local scale symmetric theory, namely Weyl's theory of gravity. We solved field equations of Weyl gravity and determined the special geometry in the outer region of galaxies. In order to understand the scale dependent description of gravitational phenomena, we compared individual terms of so called Einstein-Weyl theory and concluded that while the outer region of galaxies are described by the Weyl term, the inner region of galaxies are described by the Einstein-Hilbert term.

Gravitational lensing in Weyl gravity

“…In Ref. [11], we also claimed that our solution for the outer region of galaxies should also hold for low-density regions up to the scale of galaxy clusters. To check the validity of that claim, in this paper, we analyze the gravitational lensing in Weyl gravity by calculating the deflection angle of light from a distant source by a galaxy cluster.…”

“…In a previous work [11], we determined the geometry in the outer region of galaxies in which stars move with almost the same rotational velocity irrespective of their distance from the galactic center. Constancy of the rotational velocity might be seen due to the existence of scale symmetry.…”

“…Thus, even though Ref. [11] has no error in its mathematical approach and soundness of its result, it was expected to explain much more than the mere phenomenon of flat rotation curves of galaxies. It was outside the scope of Ref.…”

“…It was outside the scope of Ref. [11] to resolve all the astrophysical and cosmological phenomena related to dark matter, which we intend to do in time as far as it is possible. It is unjust to expect a single paper to bring explanations to countless diverse observations.…”

“…Thus, the present paper and also Ref. [11] should be thought of as part of ongoing research to understand the relevance of Weyl gravity to natural phenomena, which has a history almost as long as one of general relativity [19][20][21][22]. This paper is organized as follows.…”