The Layered Dark Structure: A Multi-Component Dark Sector Framework for Resolving the S₈ Tension

We introduce the Layered Dark Sectors with a Structuring Field (LDS-SF), a novel cosmological framework where the internal architecture of a multi-component dark sector naturally generates scale-dependent growth of structure. In this framework, the characteristic scale dependence is derived from the dominant eigenvalue, λ(k), of the dark sector's perturbation matrix. This structurally-driven mechanism modifies structure growth while preserving the standard ΛCDM background expansion and General Relativity. We provide a minimal and effective realization of this framework within a two-component DM Z₄-symmetric Inert Doublet Singlet Model (Z₄-IDSM). By integrating out different scenarios of heavy inert doublet mediator, we derive a contact-interaction Effective Field Theory (EFT) for a 60 GeV singlet dark matter candidate. This interaction manifests macroscopically as an effective sound speed c_s², which we map to the LDS-SF eigenmode evolution. We implement this system into the CLASS Boltzmann code, employing a dynamical scaling c_s²(a) ∝ a² consistent with the Effective Field Theory of Large Scale Structure (EFTofLSS). We also compute the relic density using micrOMEGAs, to further stress-test the relic abundance predictions of viable parameters. Our numerical analysis demonstrates that while the model remains indistinguishable from ΛCDM at the era of recombination, it introduces a targeted suppression of the matter power spectrum at late times (z < 10) and small scales (k > 0.1 h/Mpc). Confronting the model with Planck CMB, BAO, and growth-rate measurements, we find three instances of couplings that successfully resolve the S₈ tension, bringing the predicted amplitude into 1σ agreement with weak-lensing data from KiDS-1000 and DES. This work establishes LDS-SF as a mathematically consistent, competitive and observationally viable alternative to standard cosmology.