Bumblebee cosmology: Tests using distance- and time-redshift probes

Abstract: In modern cosmology, the discovery of the universe's accelerated expansion has significantly transformed our understanding of cosmic evolution and expansion history. The unknown properties of dark energy, the driver of this acceleration, have not only prompted extensive studies on its nature but also spurred interest in modified gravity theories that might serve as alternatives. In this paper, we adopt a bumblebee vector-tensor modified gravity theory to model the cosmic expansion history and derive predictions for the Hubble parameter. We constrain the bumblebee model parameters using observational data from established probes, including the Pantheon+ Type Ia Supernovae calibrated via the SH0ES (Supernova $H_0$ for the Equation of State) Cepheid distance ladder analysis and Baryon Acoustic Oscillations (BAO) measurements from Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2), as well as recently included cosmic chronometers (CC) and gamma-ray bursts (GRBs). The Markov Chain Monte Carlo (MCMC) sampling of the Bayesian posterior distribution enables us to rigorously constrain the bumblebee models and compare them with the standard $\Lambda \text{CDM}$ cosmology. We find that the bumblebee theory on its own can provide sufficiently good fits to the current observational data of distance- and time-redshift relations, suggesting its potential to explain the cosmic background dynamics. However, when compared to $\Lambda \text{CDM}$, the latter still outperforms the former according to the information criteria. We propose that further constraints from cosmological perturbation tests could impose more stringent constraints on bumblebee cosmology.