Celestial and Quantum Dynamics as 4D Relativistic Cloud-Worlds Embedded in a 4D Conformal Bulk: From String to Cloud Theory

Considerable efforts have been devoted to modifying gravity in order to elucidate the possible existence or nature of dark matter and dark energy, describe observational data effectively, and advance toward a theory of quantum gravity. In addition, despite its immense success, quantum field theory requires renormalization techniques and breaks down at high energies. Notably, the Planck 2018 legacy release confirmed the existence of an enhanced lensing amplitude in the cosmic microwave background power spectra, which suggests a positively curved early Universe with a confidence level more than 99%. In this study, we model the global curvature of the Universe as the curvature of a ‘4D conformal bulk’ — a geometric manifestation of vacuum energy, and regard celestial objects that induce localized curvature within the bulk as ‘4D relativistic cloud-worlds’. Employing a dual-action variational principle that incorporates both local and global curvatures, we derive interaction field equations that generalize general relativity and recover quantum behavior in the flat-bulk limit. Within this framework, gravity emerges as the local curvature of the bulk — an indicator of the field strength of vacuum energy acting on embedded quantum fields, which are described as localized geometric excitations embedded in a structured vacuum background. A visualization of the evolution of the 4D relativistic cloud-world over the conformal spacetime of the 4D bulk is presented. We apply the derived interaction field equations to model active galactic nuclei and outline testable predictions that could directly provide confirmations or falsify the framework.