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

TL;DR

This work develops a cosmological model in which a timelike Bumblebee vector field spontaneously breaks Lorentz symmetry and interacts with Tsallis holographic dark energy through a Higgs-like potential. The authors derive the modified Friedmann equations and analyze the dynamics for three nonextensive parameters $\delta = 2, 3/2, 1$, finding an inflation-like early epoch followed by a relaxation toward an equilibrium that yields late-time acceleration; in particular, the Hubble parameter evolves toward the present value $H_0$, offering a dynamical route to alleviate the Hubble tension. They estimate key parameters, including the Bumblebee mass $m_B \approx 2.55\times10^{-3}$ eV, a gravity–Bumblebee coupling $\xi \approx 2.9\times10^{-87}\ \text{J}^{-1}\text{s}^{-1}\text{m}^2$, and a Higgs-like coupling $\lambda \approx 8.35\times10^{7}\ \text{J}^{-1}\text{s}^{-1}$, under a unit background field $b$ and small $\xi$. The results show how Lorentz-violating dynamics, when combined with THDE, can produce a coherent expansion history linking inflation to the current accelerated era, offering a novel perspective on the Hubble tension within an effective field theory framework.

Abstract

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.

Figures (2)

• Figure 1: Schematic representation of the Bumblebee field dynamics governed by its potential and the interaction with Holographic dark energy.
• Figure 2: Dynamics of the Bumblebee field (normalized by the coupling constant $\xi$) and the Hubble parameter during the first seconds of cosmic evolution for the $\delta=2$ case. The difference obtained here is $b-B\sim10^{-97}$.