Considerable efforts have been devoted to modifying gravity, which aim to elucidate the possible existence or nature of dark matter and dark energy, achieve a better description of observation data, and formulate quantum gravity. In addition, despite the enormous success of the quantum field theory, the framework requires renormalization techniques and breaks down at high energies. Recently, the Planck Legacy release has confirmed the presence of an enhanced lensing amplitude in the cosmic microwave background power spectra, which prefers a positively curved early Universe with a confidence level greater than 99%. This study considers the implied positive curvature of the early Universe as the curvature of ‘the background or the 4D conformal bulk as a manifestation of vacuum energy’ and distinguishes it from the localized curvature that is induced into the bulk by the presence of celestial objects that are regarded as ‘4D relativistic cloud-worlds’. Analogously, since gravitation seems to emerge owing to spacetime curvature and does not exhibit critical characteristics shared by the other fields, it has been incorporated as the local background curvature of the bulk, due to the stress-energy of the cloud-world, affecting the embedded quantum fields that are regarded as propagating ‘4D relativistic quantum clouds’. To consider the impact of the bulk on the embedded clouds, this paper presents interaction field equations in terms of the brane-world modified gravity and the perspective of gravitization of the quantum mechanics that count for the curvature of the 4D conformal bulk as the induced gravity on the embedded 4D relativistic clouds in addition to the boundary term interactions, which could remove the singularities and satisfy a conformal invariance theory. A visualization of the evolution of 4D relativistic cloud-worlds over the conformal spacetime of the 4D bulk is presented.