Relic Density Topology as a Discriminatory Tool: A Comparative Analysis of IDM, MSSM, and NMSSM Dark Matter

Abstract

This study proposes a diagnostic mechanism based on the relic density topology to discriminate between the Inert Doublet Model (IDM), the Minimal Supersymmetric Standard Model (MSSM), and the Next-to-Minimal Supersymmetric Standard Model (NMSSM). Using a unified numerical scan with micrOMEGAs over the heavy-mass regime ($m_{x} > 300$ GeV), we contrast the phenomenological profiles of these frameworks. We demonstrate that the IDM admits a broad, stable viability plateau driven by efficient gauge couplings, while the MSSM and NMSSM typically overproduce dark matter, reaching the Planck relic density only through narrow, fine-tuned resonance channels. A quantitative fine-tuning measure reveals the IDM's viable parameter space is an order of magnitude more natural than its SUSY counterparts. Furthermore, by examining the thermal decoupling epoch ($z_{f}$) and the CMB energy-injection parameter ($p_{ann}$), we confirm that all identified viable regions are consistent with cosmological observations, and that the models exhibit different thermal history scenarios for the Universe. Our findings establish a multi-faceted discriminative framework: the IDM is characterized by a robust plateau and low fine-tuning, the MSSM by a sharp slepton-mediated annihilation dip, and the NMSSM by a diluted signature due to singlino admixture. The discovery of a heavy WIMP without sharp resonance features would therefore phenomenologically favor scalar doublet extensions over minimal supersymmetric frameworks.