Emergent Dark Matter

The work develops a complete theoretical and computational framework in which an emergent dark-matter-like component arises from quantum scalar fields in an AdS5 bulk: the projection of the bulk Weyl tensor together with a renormalized local contribution produces an effective energy–momentum component on the 4D brane. The author derives the bulk and brane equations of motion (with Robin-type boundary conditions), formulates the Sturm–Liouville spectral problem for Kaluza–Klein modes, and performs the semiclassical renormalization needed to obtain the renormalized stress tensor and nonlocal brane response. Numerically, the paper supplies reproducible pipelines: spectral solvers for KK modes, WKB acceleration of mode sums, a finite-element solver for the linearized Einstein equations in the bulk, construction of the transfer kernel, and integration with cosmological Boltzmann solvers to generate CMB and large-scale-structure predictions. The results are compared with rotation-curve, strong/weak lensing, ΔN_eff and collider bounds, parameter scans are presented, and a publicized computational environment and test suite are provided to ensure reproducibility.