Bouncing Bianchi Type I Universes with Interacting Vacuum

Abstract

We investigate the global dynamics and cosmological viability of non-singular solutions in an anisotropic Bianchi type I universe featuring an interacting vacuum energy component $V$ and a perfect fluid $ρ$, extending previous work based on a Robertson-Walker geometry. By modeling the energy-momentum transfer via a phenomenological four-vector $Q_μ$, we reduce the field equations to a four-dimensional autonomous dynamical system for the expansion rate $Θ$, total shear $σ$, energy density $ρ$, and vacuum component $V$. We examine two distinct forms for how the interaction depends on $ρ$ and $V$: a linear coupling $Q_1 \propto Θ[ξ(V_Λ- V) + χρ]$ and a non-linear coupling $Q_2 \propto Θρ(1 - V/V_Λ)$. Using a potential-energy analogy and phase-space analysis, we show that the linear model $Q_1$ naturally admits non-singular bouncing trajectories. In contrast, unlike the Robertson-Walker case, for the non-linear interaction $Q_2$, invariant boundary surfaces in phase space strictly constrain the domain of expansion ruling out cosmological bounce scenarios for physical matter configurations.