Deformed Special Relativity in Light of the Unruh Effect

We propose a modified relativistic dynamics framework for a particle undergoing a proper acceleration a immersed in a vacuum background of temperature T. Within this framework, the Unruh effect dictates that the accelerated observer perceives the vacuum as a thermal bath. By associating the Planck temperature TP and its corresponding energy scale EP with an invariant, maximal Planck acceleration aP, we reformulate the dynamics under the aegis of Doubly Special Relativity (DSR). In this setting, the acceleration-induced thermal background acts as a physical preferred frame, necessitating a quantum–gravitational correction to the mass–energy equivalence E=mc2. This derivation yields the Magueijo–Smolin dispersion relation, here reinterpreted through a cosmological–thermodynamic lens, where the thermal vacuum emerges dynamically from particle acceleration. Furthermore, we demonstrate that the speed of light diverges as T→TP in the early universe, driven by inflation at the Planck acceleration scale. This rapid decay of c during the inflationary epoch provides a novel mechanism for Varying Speed of Light (VSL) theories, offering a robust alternative for resolving the horizon problem.