TATE: A Coherent-Energetic Theory of Emergent Time within the TDCAED Cosmological Framework

TATE: A Coherent-Energetic Theory of Emergent Time within the TDCAED Cosmological Framework explores a speculative but mathematically structured model in which time is interpreted not as a fundamentally geometric dimension, but as an emergent manifestation of coherent energetic transfer within a primordial nonlinear field. Developed within the broader conceptual architecture of the TDCAED (Teoría Domingo Cuevas-Andújar del Estruendo Divino), the paper proposes that the observable flow of time arises from the organization, propagation, and degradation of coherence in the foundational structure of the universe. The work introduces the TATE framework (Absolute Time of Energetic Transfer and Equilibrium) and formulates its dynamics through a nonlinear Klein–Gordon-type equation capable of generating stable solitonic solutions. These solitons are interpreted as localized packets of coherent temporal-energy structure, potentially associated with stable matter configurations, dark matter condensates, or cosmological coherence domains. The paper develops: a nonlinear field-theoretic foundation for TATE, an effective Lagrangian formalism, entropy-coherence coupling relations, emergent temporal metrics, gravitational extensions through stress-energy coupling, and cosmological implications involving inflation, dark matter, and the arrow of time. Special attention is given to the relationship between coherence, entropy, and temporal stability. Within this framework, entropy is reinterpreted as degradation of coherent temporal organization, while gravitation acts as a modulator of coherence density within spacetime. The model draws mathematical inspiration from nonlinear wave mechanics, scalar field cosmology, soliton theory, and emergent spacetime approaches, while proposing a distinct ontological interpretation centered on coherence as a primary physical principle. Although exploratory and currently unverified experimentally, the framework aims to provide a structured conceptual basis for future investigations into: emergent time, nonlinear cosmology, coherence-based gravity, solitonic matter structures, and informational-energy interpretations of spacetime. This publication is intended as a theoretical preprint for academic discussion and interdisciplinary exploration in cosmology, mathematical physics, nonlinear dynamics, and philosophy of physics. Author: Domingo Cuevas-Andújar