Dynamical constraints on variable vacuum energy in Brans-Dicke theory

TL;DR

The paper investigates late-time cosmic acceleration within Brans-Dicke (BD) gravity by incorporating a dynamical vacuum energy density Λ that evolves with cosmic expansion. It analyzes two phenomenological models: a hybrid vacuum law Λ(t) = α H^2 + β \,dot{H} and a power vacuum law Λ(H) = α_1 H^n, deriving analytical expressions for the Hubble parameter, cosmographic parameters, and the age of the Universe. The hybrid model yields a constant deceleration parameter and cannot reproduce the observed transition to acceleration, while the power-law model produces a redshift-dependent q(z) and an evolving ω_eff that transitions from matter-dominated to a ΛCDM-like de Sitter future, with present values q_0 ≈ -0.516 and ω_eff(z=0) ≈ -0.592; jerk and snap deviate modestly from ΛCDM but converge at late times. The analysis finds a present age t_0 ≈ 13.12 Gyr, and demonstrates that BD dynamics with a running vacuum can account for observational expansion history, with PVL offering a viable alternative to ΛCDM in this framework.

Abstract

In this research work, we investigate the late-time accelerated expansion of the universe within the framework of Brans-Dicke theory by considering dynamical vacuum energy models with a time-varying cosmological constant. Two vacuum energy models are studied, namely the hybrid vacuum law $Λ(t)=αH^{2}+β\dot{H}$ and the power vacuum law $Λ(H)=α_{1}H^{n}$, where $α$, $β$, $α_{1}$ and $n$ are free parameters. We derive analytical solutions for the Hubble parameter and other relevant cosmological quantities. The evolution of the deceleration parameter, the effective equation of state, the cosmographic parameters and the present age of the universe are also analyzed.

Figures (4)

• Figure 1: Deceleration parameter $q(z)$ versus $z$.
• Figure 2: Effective EoS parameter ($\omega_{eff}$) versus $z$.
• Figure 3: Jerk parameter ($\mathit{j}$) versus $\mathit{z}$.
• Figure 4: Snap parameter ($\mathit{s}$) versus $\mathit{z}$.