Astrophysics With Weyl Gravity

We aim to explain some astrophysical phenomena in low density astronomical regions without invoking dark matter. We propose that the effective theory of gravity could have individual terms which become dominant in respective regions, and effectively describe the gravitational phenomena there. In the outer region of galaxies, the effective theory of gravity could be the Weyl gravity, which is the unique local scale symmetric metric theory. Inside the bulge, however, general relativity is the effective description of gravity. Hence, we propose the Einstein-Weyl gravity as a scale-dependent effective description of the gravitational phenomena. At high densities or high curvature regions, the effective description for gravity is provided by Einstein's general relativity, whereas in the low density regions it is provided by the Weyl gravity. We then solve the field equations of Weyl gravity in the outer region of galaxies and determine the geometry in which stars move with the same rotational velocity independent of their distance from the center of the galaxy. We then utilize this metric solution to calculate the deflection angle of light from a distant source by a galaxy cluster. The deflection angle calculated in Schwarzschild-de Sitter-like space includes contributions from both the cosmological constant Lambda and the Mannheim-Kazanas parameter gamma. There are conflicting results on the deflection angle for light in Weyl gravity in the literature. Our result agrees with some and disagrees with many. We point out possible reasons for this discrepancy.