Cosmological implications of Bumblebee theory on an FLRW background

TL;DR

This work studies the cosmological implications of Bumblebee gravity on a flat FLRW background, focusing on phase-space structure, critical points, and their stability. By employing a cosmic triad to preserve isotropy and a simplified action with a single coupling α, the authors derive the modified Friedmann equations and define an effective dark-energy sector through ρ_de and p_de, along with w_de and statefinders r and s. A dynamical-systems analysis reveals three fixed points corresponding to radiation, matter, and a late-time accelerating attractor; stability requires $1/6 < \alpha < 1/2$, and SN data (Pantheon+SH0ES) constrain α to ≈ 0.347, yielding a distance-redshift relation that closely tracks ΛCDM. Statefinder diagnostics show convergence to the ΛCDM point (r,s) → (1,0) at late times, while deviations appear at higher redshift, indicating Bumblebee dynamics can mimic ΛCDM asymptotically but leave potentially observable imprints in the early and intermediate evolution of the Universe.

Abstract

We investigate some cosmological implications at background level of the Bumblebee model. The phase-space, the critical points and their stability are analyzed in detail applying well-established dynamical system techniques. What is more, upon comparison to available supernovae data, the best fit numerical value of the unique free parameter of the model is determined. We show graphically all the cosmological quantities of interest versus red-shift, such as the deceleration parameter, dark energy equation of state parameter, etc. The statefinders and the age of the Universe are also computed. Finally, a comparison to the $Λ$-CDM model is made as well.

Figures (7)

• Figure 1: The phase space of $x$ versus $y$ for $\alpha = 0.347$ is shown, where the critical points are marked as red dots with their respective labels. Each trajectory represents the evolution of the Universe for different initial conditions. In particular, the black line corresponds to a Universe initialized with $x_i = 8.0 \times 10^{-9}$, $y_i = 1.645 \times 10^{-3}$, and $\varrho_i = 0.999825$. The green region highlights the domain of accelerated expansion. Since the dynamical system is symmetric under the transformation $y \to -y$, we restrict the analysis to the upper half-plane ($y>0$) without loss of generality. In this way, only the three relevant critical points of Table \ref{['table1']} are displayed, which are sufficient to reproduce the thermal history of the Universe.
• Figure 2: The phase space for $\alpha = 0.347$ is shown, where the critical points are marked as red dots with their respective labels. Each trajectory represents the evolution of the Universe for different initial conditions. In particular, the black line corresponds to a Universe initialized with $x_i = 8.0 \times 10^{-9}$, $y_i = 1.645 \times 10^{-3}$, and $\varrho_i = 0.999825$.
• Figure 3: Confidence levels at the $1\sigma$ and $2\sigma$ limits for the Bumblebee model obtained from the PantheonPlus+SH0ES dataset. The contours show the marginalized constraints on $(H_0,\ \Omega_m,\ M_B,\ \alpha)$.
• Figure 4: Distance modulus versus red-shift. Shown are: Data points, Bumblebee model (solid curve) and $\Lambda$-CDM model (dashed curve).
• Figure 5: Deceleration parameter (left panel) and dark energy equation-of-state parameter (right panel) versus red-shift. In both panels the dashed curves correspond to the $\Lambda$-CDM model.