Deformed Special Relativity in Light of the Unruh Effect

In the paper, we propose a modified relativistic dynamics for a particle moving with an acceleration $a$ with respect to a background frame of vacuum with a temperature $T$. This background temperature is detected by such an accelerated particle according to Unruh effect, working like a background thermal bath. The Planck temperature $T_P$ is associated with the Planck energy $E_P$, which is obtained for the so-called Planck acceleration $a_P$, being maximum and unattainable (invariant). Thus, the acceleration in the scenario of a deformed special relativity (DSR) leads to a thermal background field that represents a preferred frame. Hence, the energy $E=mc^2$ needs a correction close to the Planck energy $E_P$, so that the well-known Magueijo-Smolin energy equation is obtained. However, it is interpreted within a cosmological and thermodynamic scenario where a thermal vacuum arises to the accelaration of the particle. Furthermore, we also show that the speed of light has diverged at the beginning of the universe with Planck temperature when the inflation occurred due to the Planck acceleration. Therefore, there was a rapid decrease of the speed of light during the cosmic inflation, which contradicts the varying speed of light (VSL) theories used to explain the so-called horizon problem.