Relational Coherence as a Foundation for Emergent Dark Energy Mapping Coherence Dynamics to Phenomenological Cosmology

This work presents a coherence-based approach to cosmology within the Relational Coherence Cosmology (2PS) framework, proposing that late-time cosmic acceleration arises as an emergent phenomenon rather than from a fundamental cosmological constant. We introduce a dynamical coherence field, denoted by (x, t), representing the degree of relational organization of the underlying physical system. Within this framework, the dark energy sector is interpreted as an effective manifestation of coherence dynamics, rather than as a fundamental component of the universe. We construct explicit mappings between the evolution of the coherence field and phenomenological emergent dark energy models, including phenomenologically emergent dark energy (PEDE), critically emergent dark energy (CEDE), and generalized emergent dark energy (GEDE). Smooth emergence, critical activation, and flexible late-time behaviors are shown to arise as distinct dynamical regimes of the coherence field. Using toy expansion histories and cosmological observables such as the normalized Hubble function E (z), the deceleration parameter q (z), and the luminosity distance dL (z), we demonstrate that the coherence-based framework reproduces the same background behavior as the standard CDM model while offering a different physical interpretation. This work establishes a conceptual and dynamical bridge between phenomenological cosmology and a relational coherence-based description of physical systems. It suggests that the cosmological constant may be interpreted as an emergent parameter associated with the asymptotic regime of coherence. The results provide a foundation for extending the framework toward structure formation, perturbation theory, and galaxy-scale dynamics, offering a potential unifying perspective on emergent dark energy and large-scale cosmological behavior.