SHADOWS AND LIGHT: REINTERPRETING GRAVITATIONAL PHENOMENA THROUGH WEYL GEOMETRY AND CONFORMAL GRAVITY

This thesis investigates the potential of Weyl geometry and conformal gravity to provide alternative explanations for phenomena traditionally attributed to dark matter and gravitational lensing. Through a rigorous examination of Weyl geometry's origins and development, alongside a detailed analysis of modified gravity theories incorporating local conformal symmetry, we explore the implications of these theories for cosmology and astrophysics. The work delves into the mathematical underpinnings of conformal rescaling in Minkowski spacetime and its impact on the geodesics of light and matter, shedding light on the geometric nature of spacetime itself.

Applying these theoretical insights, the thesis critically assesses the Bullet Cluster's gravitational lensing effects, suggesting that conformal gravity could offer a plausible alternative to the dark matter hypothesis. This proposition challenges the conventional understanding of cosmic mass and energy distribution, prompting a reevaluation of gravitational lensing phenomena.

None of modified gravity theory without dark matter have explain the discrepancy between the mass map in galaxy clusters reconstructed form X-ray and gravitational lensing effect to a satisfactory level before, and our result fill in this blanks by introducing a different mechanism of background image distortion, which can fit the galaxy image pattern around the Bullet Cluster well.  

The research presented not only contributes to theoretical physics by offering new perspectives on gravity and cosmology but also sets the stage for future investigations. It underscores the importance of exploring alternative theoretical frameworks in addressing some of the most pressing questions in modern physics, such as the nature of dark matter, the unification of gravity with quantum mechanics, and the fundamental structure of the universe.

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