Cosmic evolution from Lorentz-violating bumblebee dynamics and Tsallis holographic dark energy

In this work, the behavior, evolution, and expansion of the universe are investigated within a Lorentz-violating framework driven by Tsallis holographic dark energy. The cosmological extension is implemented through a spontaneously symmetry-breaking Bumblebee field, which is assumed to play a fundamental role in the dynamics of the universe. Estimates for key Lorentz-violating quantities are obtained, and the evolution of the Hubble parameter is analyzed from the early universe era to the present epoch. This formulation provides an alternative perspective on the Hubble tension.