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 $Λ$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 $Λ$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.

Figures (3)

• Figure 1: Posterior distributions of cosmological parameters $\tilde{\xi}_1$, $\alpha$, $H_0$, $\Omega_{{\mathcal{K}}0}$ for the spatially curved (left panel) and spatially flat ($\Omega_{{\mathcal{K}}0}=0$, right panel) bumblebee models, constrained by four individual cosmological probes: gamma-ray bursts (GRBs, dashed gray contours), cosmic chronometers (CC, solid yellow contours), Type Ia Supernovae (SNe Ia, solid red contours), and Baryon Acoustic Oscillations (BAO, solid cyan contours). The contours represent the 68% and 95% confidence regions derived from MCMC sampling.
• Figure 2: Posterior distributions of the same cosmological parameters as in Figure \ref{['fig:posterior_individual']}, for the spatially curved (left panel) and spatially flat ($\Omega_{{\mathcal{K}}0}=0$, right panel) bumblebee models. Results are shown for joint constraints including group 1 (blue contours), standard probes: SNe Ia + BAO and group 2 (green contours) with all 4 probes. The contours represent the 68% and 95% confidence regions from MCMC sampling and illustrate how combining multiple probes breaks degeneracies.
• Figure 3: The best-fit prediction using all four observational probes jointly for both spatially curved and flat bumblebee model, in comparison with the standard $\Lambda$CDM model. All data points are plotted as gray filled circles with black error bars. Top left panel shows the distance modulus $\mu$ versus redshift $z$ for Pantheon+ Type Ia supernovae. Top right panel displays the angle‑averaged BAO signal $D_V/r_{\mathrm{d}}$ versus redshift $z$ from DESI DR2 measurements. Bottom left panel presents the Hubble parameter $H(z)$ versus redshift $z$ derived from CC observations. Bottom right panel depicts the Amati linear relation from GRBs. In every panel the solid blue line represents the best‑fit prediction of the curved bumblebee model, the solid green line represents the flat bumblebee model, and the red dashed line represents the $\Lambda$CDM model.