Bouncing Bianchi Type I Universes with Interacting Vacuum

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 $\rho$, extending previous work based on a Robertson-Walker geometry. By modeling the energy-momentum transfer via a phenomenological four-vector $Q_{\mu }$, we reduce the field equations to a four-dimensional autonomous dynamical system for the expansion rate $\mathrm{\Theta }$, total shear $\sigma$, energy density $\rho$, and vacuum component $V$. We examine two distinct forms for how the interaction depends on $\rho$ and $V$: a linear coupling $Q_1\propto \mathrm{\Theta }[\xi (V_{\mathrm{\Lambda }}-V)+\chi \rho ]$ and a non-linear coupling $Q_2\propto \mathrm{\Theta }\rho (1-V\mathrm{/}{V}_{\mathrm{\Lambda }})$. 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.