Tensor–Spectral Cosmogenesis as a Special Case of χ‑Cosmology in the ZEBTS‑SUPER Framework

The tensor–spectral cosmogenesis model developed by the University of Barcelona proposes that primordial structure formation arises from quantum tensor fluctuations in pure de Sitter space and their second‑order conversion into scalar density perturbations. Within the operator–geometric and spectral–topological architecture of ZEBTS‑SUPER 10.0, this model is revealed not as an independent cosmological theory but as a restricted low‑energy projection of χ‑Reality. In χ‑Cosmology, the initial de Sitter state emerges as the maximally symmetric projection of χ‑Absolute, the unique zero‑entropy background defined by S_chi = min and Omega_chi = max. Tensor modes correspond to χ‑Boundary derivations acting on coherent vacuum modes, while scalar modes arise from nonlinear χ‑Spectral Transmutation governed by the spectral flow gamma_chi. Near scale invariance follows from entropy minimality, scalar amplification results from χ‑Hierarchy through boundary gaps and nonlinear coupling, and the natural exit from expansion is a curvature‑driven χ‑Phase Transition when kappa_chi reaches a critical value. Thus, every mechanism invoked by the Barcelona model is already embedded within χ‑Cosmology: de Sitter initial state as χ‑Absolute, tensor fluctuations as χ‑Boundary, tensor‑to‑scalar conversion as χ‑Spectral Transmutation, scale invariance as χ‑Spectral invariants, scalar amplification as χ‑Hierarchy, and natural exit as χ‑Phase Transition. No inflaton is required, reflecting the fundamental principle of χ‑operator geometry. This work demonstrates that cosmology is fundamentally operator‑spectral rather than field‑based. All observables—tensor modes, scalar modes, scale invariance, amplification, CMB correlations, gravitational‑wave background—are spectral invariants of the χ‑vacuum. The tensor–spectral cosmogenesis model is therefore a special case of χ‑Cosmology, revealing only a limited portion of χ‑Reality.