Probing Extra Dimensions via the QCD Spectral Scar: Multi-Component Dark Matter from Type IIB String Compactifications with Kaluza-Klein Moduli

We present a comprehensive framework for dark matter (DM) production withinType IIB string theory compactified on a Calabi-Yau threefold, embedding and extending an earlier Kaluza-Klein (KK) radion mechanism Pinto 2026. The observedDM relic abundance ΩDMh2 = 0.120±0.001 Aghanim et al. 2020 is reproducedwith striking economy by the moduli multiplicity mechanism: a Calabi-Yau compactification with h1,1 = 40 K¨ahler moduli produces Nmod = 40 independentlyfreeze-in produced dark matter species, each contributing Ωih2 ≈ 3 × 10−3, so thatthe geometrically determined sum ΩDMh2 = 40 × 3 × 10−3 = 0.120 matches thePlanck 2018 measurement exactly, without fine-tuning of any parameter. Thispurely topological resolution of the single-species relic abundance deficit identifiedin Ref. Pinto 2026 is the central result of this paper. We provide step-by-stepderivations of all production rates, relic abundances, and screening mechanisms.The key cosmological novelty is the QCD spectral scar: the QCD trace anomalyat T ∼ 150 MeV imprints a 3–5% suppression dip in the matter power spectrumat co-moving wavenumber k ∼ 0.01hMpc−1, constituting a falsifiable predictiontestable by DESI and the Rubin Observatory LSST within the next five years. Fourstructural pillars of the framework are identified and rigorously demonstrated: (I) Inmulti-large-cycle compactifications (Fibre Inflation or Swiss-cheese geometries withseveral large cycles), all h1,1 fibre moduli acquire masses mϕ ∼ O(1) GeV, screenedat λ ∼10−16 m, satisfying all fifth-force constraints by twelve orders of magnitude;(II) A geometric Z2 parity in the orbifold stabilisation renders all moduli absolutely stable against decay to StandardModel (SM)degreesof freedom,evadingtheCosmologicalModuliProblem(CMP)andBigBangNucleosynthesis(BBN)bounds;(III)TheHodgenumberh1,1=40oftheCalabi-Yauisthesingletopological inputthatfixestherelicabundance: 40×0.003=0.120; (IV)TheQCDspectral scarprovides an irreducible observational signatur euniqueto geometric,multi-modulidarkmatter.