Elastic Universe Theory: Quaternionic and Elastic Unification of Physical Realitym

This work presents a comprehensive formulation of the Elastic Universe Theory (TUE), a unifying physical model where all observed phenomena—mass, time, energy, fields, and space-time curvature—emerge from the elastic deformation of the physical vacuum. The theory proposes that the vacuum is not empty but structured, continuous, and capable of tension and quantized oscillation.<br>We compare and integrate TUE with the quaternionic formalism developed by Danielewski and Sapa (2020), demonstrating that the quaternionic wavefunction naturally encodes the same internal geometry assumed by the elastic field. By representing the elastic displacement field as a quaternion , we show that mass, spin, curvature, and gauge interactions arise from internal rotation, amplitude, and orientation of this unified field.<br>The article includes seven chapters: theoretical foundations, formal postulates, detailed comparison with the Polish quaternionic model, structural unification, physical implications, cosmological consequences, and future research directions. The final unified model reproduces major observable constants (H₀, particle masses, CMB features) within experimental margins and proposes a falsifiable and testable geometric framework.<br>All content is original by the author Andrea Zanette, with editorial and mathematical assistance by ChatGPT-4 (OpenAI). This document is intended for open-access publication on Figshare.