Resolving Cosmological Singularities and the Hubble Tension via Finsler-Maxwell TR Gravity

AbstractThis thesis provides a comprehensive mathematical and physical development of the Thermo-Relativistic (TR) extension of spacetime. Operating strictly within the tangent bundle TM of Finsler geometry, this framework replaces the static speed of light c with a dynamic, environment-dependent local limit speed 𝑉𝑙𝑖𝑚(𝑣, 𝜈, 𝑇). By setting the coupling constant to its exact topological invariant value 𝛼 =1/4𝜋 and introducing an Infrared (IR) cosmic boundary alongside Ultraviolet (UV) Planck bounds, we resolve the primordial singularity through a Planck-scale Big Bounce and predict a causally protected Big Crush phase contraction. The field equations and modified FinslerMaxwell electrodynamics are derived, showing parametric vacuum amplification and light-cone broadening during the contraction era.