Prediction P12: Characteristic Signatures of Topological Defect Dark Matter Halos - Cosmological Predictions Based on the Ξ-Field Topological Defect Model

The cold dark matter (CDM) paradigm faces persistent challenges on small scales: the cusp-core problem, missing satellite galaxies, and substructure lensing anomalies. Self-interacting dark matter (SIDM) is currently the leading candidate solution. This paper proposes a distinguishable alternative framework: dark matter consists of topological defects (1D cosmic strings / 2D domain walls / 0D monopoles) formed during spontaneous symmetry breaking of the Ξ-field in the early Universe. Unlike CDM particles and SIDM, topological defects possess nonzero internal pressure (p≠0), a characteristic spatial scale, and an effective tension that evolves with the background cosmic expansion. We present four testable cosmological predictions: (1) the matter power spectrum P(k) exhibits characteristic oscillations on nonlinear scales (k ~ 0.1–1 h/Mpc) with relative amplitude 3%–8%; (2) the concentration-mass-redshift relation c(M,z) is systematically lower than ΛCDM predictions at high redshift (z>2), with the offset coupled to the dark energy equation-of-state evolution; (3) the weak-lensing shear correlation function xi_±(θ) exhibits residual patterns at specific angular scales, testable with Euclid DR1 (October 2026); (4) the triaxiality distribution of dark matter halos deviates from CDM: 1D-string-dominated regions favor prolateness, while 2D-domain-wall-dominated regions favor oblateness. All four predictions are clearly distinguishable from SIDM. Falsification conditions are specified with Euclid DR1 and LSST early data as primary targets.

topological defect dark matter, cosmic strings, domain walls, halo density profile, matter power spectrum, Euclid, weak lensing, halo triaxiality, Ξ-field, Life Panorama