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Considerable efforts have been devoted to modifying gravity, which aim to elucidate the possible existence or nature of dark matter and energy, describe observational data more effectively, and formulate quantum gravity. In addition, despite the immense success of quantum field theory, the framework requires renormalization techniques and breaks down at high energies. Recently, the Planck legacy 2018 release confirmed the existence of an enhanced lensing amplitude in cosmic microwave background power spectra, which prefers that the early Universe had a positive curvature with a confidence level higher than 99%. This study considers the implied primordial curvature as the global curvature or curvature of “4D conformal bulk as a manifestation of vacuum energy” and distinguishes it from the localized curvature that is induced in the bulk by the presence of celestial objects that are regarded as ”4D relativistic cloud-worlds”. Analogously, because gravity appears to emerge owing to spacetime curvature and does not exhibit critical characteristics that are shared by other fields, it has been incorporated as the bulk’s local curvature affecting embedded quantum fields that are regarded as propagating “4D relativistic quantum clouds”. To consider the effects of the bulk on embedded clouds, this paper presents interaction field equations in terms of the brane-world modified gravity and perspective of geometrization of quantum mechanics; wherein gravity is manifested by the curvature of 4D conformal bulk as an indicator of the field strength of vacuum energy on the embedded 4D relativistic clouds in addition to the boundary interactions, which could eliminate the singularities and satisfy a conformal invariance theory. A visualization of the evolution of the 4D relativistic cloud-world over the conformal spacetime of the 4D bulk is presented. The standard said theories are recovered from the interaction field equations, whereas experimental conditions are recommended to directly falsify or provide confirmations to the derived equations.