Æther Model – Structural breakdown of comoving modes and primordial spectra under autosimilar extrapolation

This technical report (written in Spanish) analyzes the mathematical and empirical consistency of the standard autosimilar extrapolation used in the inference of the primordial cosmological spectrum within effective field theory frameworks. The work focuses on the dynamical operator governing scalar primordial perturbations and examines the conditions under which its hyperbolic structure—required for defining comoving oscillatory modes, physical frequencies, and adiabatic initial states—remains valid when extrapolated toward arbitrarily early times. It is shown that extending autosimilar spectral extrapolation toward the primordial regime generically forces the effective operator to lose hyperbolicity through the degeneration of its temporal kinetic structure. This loss implies a structural collapse of the notion of comoving mode and of primordial frequency, rendering the standard definition of a global autosimilar spectrum mathematically ill-defined beyond a finite domain of validity. The result does not correspond to quantitative corrections of the spectral index, slow-roll parameters, or model-dependent inflationary features. Instead, it identifies a qualitative breakdown of the effective formalism underlying primordial spectral inference, independent of specific inflationary potentials or microscopic assumptions. No new degrees of freedom, ad hoc prescriptions, or ultraviolet completions are introduced. The analysis leads to a precise, non-parametric, and falsifiable empirical criterion based on the functional incoherence of spectral extrapolation, providing a test for the finite domain of validity of the standard primordial spectrum. Within the Æther research program, this report constitutes a second instance of structural empirical verification, showing how the limits of an effective cosmological description can be identified through observable breakdowns of spectral coherence rather than through parameter fitting or model extension.